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What is the shortest Ph.D. thesis? [closed]
The question is self-explanatory, but I want to make some remarks in order to prevent the responses from going off into undesirable directions.
It seems that every few years I hear someone ask this question; it seems to hold a perennial fascination for research mathematicians, just as quests for short proofs do. The trouble is that it has strong urban-legend tendencies: someone will say, "So-and-so's thesis was only $\epsilon$ pages long!" where $\epsilon \ll 1$ . It will often be very difficult to confirm or disconfirm such claims, since Ph.D. theses are often not even published, let alone readily available online. If you Google around for a while, as I did, you will find many dubious leads and can easily waste a lot of time on wild goose chases. Frankly, I'm a bit fed up with this state of affairs. I am therefore asking this question on MO in the hope that doing so will put this old question to rest, or at least establish provable upper bounds.
I would therefore request that you set yourself a high standard before replying. Don't post a candidate unless you're sure your facts are correct, and please give some indication why you're so sure. Read the meta discussion before posting. (Note that the meta discussion illustrates that even a MathSciNet citation isn't always totally definitive.) Include information about the content and circumstances of the thesis if you know it, but resist the temptation to gossip or speculate.
I'm not making this question community wiki or big-list because it should ideally have a definite answer, though I grant that it's possible that there are some borderline cases out there (perhaps there are theses that were not written in scholarly good faith, or documents that some people would regard as equivalent to a Ph.D. thesis but that others would not, or theses in subjects that are strictly speaking distinct from mathematics but that are arguably indistinguishable from mathematics dissertations).
Finally, to anticipate a possible follow-up question, there is a list of short published papers here (search for "Nelson"). Note that the question of the shortest published paper is not as urban-legendy because the facts are easier to verify. I looked up the short papers listed there myself and found them to be quite interesting. So in addition to trying to settle an urban legend, I am hoping that this question will bring to light some interesting and lesser known mathematics.
- ho.history-overview
- 9 $\begingroup$ I think it really should be CW. It makes no sense to me that the shorter the proposed candidate, the more reputation the proposer will get. It will also lower the temptation for people to post gossipy stuff. $\endgroup$ – Alex B. Commented Feb 8, 2011 at 15:31
- 3 $\begingroup$ The only reasonable interpretation of the question is extremely short theses in general, because there is more than one measure of the length of a thesis. Moreover in some cases it's debatable whether a particular document really is a thesis or the full thesis. It realy should be CW. $\endgroup$ – Greg Kuperberg Commented Feb 8, 2011 at 15:40
- 3 $\begingroup$ How would you like to count? Do all the cover pages, table of contents, abstract, etc. count? How about references? Or do you begin with the introduction and only include the content? $\endgroup$ – Noah Stein Commented Feb 8, 2011 at 16:33
- 5 $\begingroup$ -1. This question is terrible. I'm sure I could reformat my thesis in a silly font size to make it have a ludicrously small number of pages. $\endgroup$ – Peter McNamara Commented Feb 8, 2011 at 19:50
- 8 $\begingroup$ @Peter McNamara: you probably could, but I'm pretty certain that this is not the issue being discussed here. Anyway, most universities have specific formatting standards and would not let you submit it in this form. $\endgroup$ – Thierry Zell Commented Feb 8, 2011 at 20:05
9 Answers 9
David Rector's thesis ("An Unstable Adams Spectral Sequence", MIT 1966) is 9 pages, according to the record at the MIT library . I haven't seen the actual thesis for many years, but I'm pretty the actual mathematical content takes about 3 pages total, and is largely identical to the published version in Topology (1966, same title, doi link: https://doi.org/10.1016/0040-9383(66)90025-5 ), which is 3 pages plus bibliography. (Dan Kan, his advisor, likes short papers.)
- 2 $\begingroup$ Probably not a coincidence. $\endgroup$ – Tyler Lawson Commented Feb 8, 2011 at 20:25
- 3 $\begingroup$ Accepted provisionally. Enough people seem instinctively annoyed at this question that it seems likely to be closed soon (despite the fact that I'm asking it on MO in order to prevent its proliferation elsewhere). It doesn't seem likely that a stronger candidate will emerge before then. Ideally I'd like to examine the thesis myself before accepting the answer but I don't feel like purchasing it and it may be a while before my next trip to Boston. $\endgroup$ – Timothy Chow Commented Feb 9, 2011 at 15:56
- 4 $\begingroup$ Aside from the library copy, there should be a slightly more accessible copy in the MIT Math reading room. (They used to keep copies of theses there, and I assume they still do.) Maybe somebody reading this could wander down the hall and take a look. :) $\endgroup$ – Charles Rezk Commented Feb 9, 2011 at 18:55
- 31 $\begingroup$ I'm in the reading room now. Rector's thesis comprises a title page, an abstract page, a table of contents page, 7 pages of math, a bibliography page (8 refs.), and a biographical note page. The MIT library record's "9 leaves" exclude the title/abstract/contents, which are not numbered. Except for some trivial changes in wording in the intro, the mathematical part is indeed identical to the 4-page Topology paper, vol. 5 (1966), 343-346. The thesis occupies more space since it's manually typed; not including section titles, the 4 sections are respectively 18, 23, 42, and 36 typewritten lines. $\endgroup$ – Timothy Chow Commented Aug 19, 2011 at 18:44
- $\begingroup$ 119 typewritten lines! $\endgroup$ – David Roberts ♦ Commented Oct 14, 2022 at 10:53
John Nash's thesis was 26 pages, and had two references in the bibliography.
Edmund Landau's thesis was 13 pages long.
- $\begingroup$ There is an English translation here: arxiv.org/PS_cache/arxiv/pdf/0803/0803.3787v2.pdf That document is 17 pages (including title page, etc.). $\endgroup$ – Zach N Commented Feb 8, 2011 at 18:06
- 2 $\begingroup$ For a link to a scanned version of Landau's thesis see here gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN317979566 The document has 18 pages, of which 2 are completely empty, indeed the catalogue of the libraries of Berlin gives 16 pages as lengths. (the French national library catalogue gives 18). Moreover, one page is a title page, one is a dedication, and one is a vita. So, depending on what one actually counts, 18, 16, or 13. According to library catalogues 16 or 18. $\endgroup$ – user9072 Commented Feb 8, 2011 at 18:15
I believe the shortest PhD thesis is of Burt Totaro "Milnor K-theory is the simplest part of algebraic K-theory", 12 pages.
Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989; published as: K-Theory 6 (1992), 177-189 ( Portico archived version ).
Burt Totaro's webpage at Cambridge , including a pdf of the published version .
- 1 $\begingroup$ its complete thesis. I gave two references here, Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis, University of California, Berkeley, 1989 and K-Theory 6 (1992), 177-189 $\endgroup$ – J Verma Commented Feb 8, 2011 at 17:43
- 2 $\begingroup$ I noticed, but the reference to the actual thesis does not have a page numbers (and it is somewhat surprising that the number of pages did not change from the thesis to K-theory's format) :) $\endgroup$ – Mariano Suárez-Álvarez Commented Feb 8, 2011 at 17:45
- 16 $\begingroup$ Totaro's 1989 thesis is titled "K-theory and algebraic cycles" and, according to ProQuest, is 20 pages. If your university library subscribes to ProQuest, you can see a PDF preview of the thesis by searching for "Totaro, Burt" in the Dissertations and Theses database. $\endgroup$ – Zach N Commented Feb 8, 2011 at 18:02
- 4 $\begingroup$ You can download it on mathscinet. It has 16 numbered pages, incl. 1 page of bibliography. Definitions start on page 1 though, not much of an introduction. $\endgroup$ – fherzig Commented Feb 9, 2011 at 2:58
- 1 $\begingroup$ I downloaded the thesis from ProQuest. It comprises a signature page, a title page, an abstract page, an epigram page, 15 pages of (TeXed) math, and a bibliography page. Short, but not as short as David Rector's thesis. $\endgroup$ – Timothy Chow Commented Aug 19, 2011 at 19:00
This is not really an answer because these PhD's were never actually written, but anyway: in his book A mathematicians miscellany (in the chapter on math with minimum raw material) Littlewood gave 2 examples that could have been 2-line PhDs:
(1) Cayley's projective definition of length
(2)Theorem: An integral function never 0 or 1 is a constant. Proof: $\exp(i\Omega(f(z)))$ is a bounded integral function. ($\Omega$ is inverse to the elliptic modular function.)
- 3 $\begingroup$ Richard, perhaps you overlooked that Gerry Myerson already gave this example on the meta discussion? $\endgroup$ – Timothy Chow Commented Feb 8, 2011 at 15:53
- 19 $\begingroup$ I don't think it is reasonable to expect people to have read all the meta discussion before posting on a regular thread. This is a sort of fluff question, so it doesn't matter much, but in general I think it should be fine to repost answers from meta, so that the main thread has the most complete record of answers to the question. $\endgroup$ – David E Speyer Commented Feb 8, 2011 at 16:52
- 7 $\begingroup$ While I agree with David Speyer in general, I also do not think this should have been posted as an answer to this particular question, given the questioner's emphasis on restricting the scope of the question. $\endgroup$ – Charles Staats Commented Feb 8, 2011 at 17:27
- 6 $\begingroup$ @David: I too would agree that in general it’s not reasonable to expect people to read meta discussions on questions before answering them. But this question specifically asks us to, and gives good reasons for it. $\endgroup$ – Peter LeFanu Lumsdaine Commented Feb 8, 2011 at 20:18
- $\begingroup$ (2) is a trivial corollary of Picard's little theorem. $\endgroup$ – tst Commented Jun 13, 2017 at 3:06
I already posted this on meta where there was some discussion of whether the page count was correct. My guess is that it is, so I will post it here too:
MR2615548 Martens, Henrik Herman Buvik A NEW PROOF OF TORELLI'S THEOREM. Thesis (Ph.D.)–New York University. 1962. 12 pp.
- 8 $\begingroup$ Compared to that, the thesis of his student Kristian Seip was a massive tome, weighing in at 30 pages. $\endgroup$ – Harald Hanche-Olsen Commented Feb 9, 2011 at 7:56
Kurt Gödel seems to be a good candidate for this "prize".
Let me quote from this review (see Page 74) of Kurt Gödel Collected Works.
The first three works of Godel in this volume are his dissertation of 1929 ( twenty-one pages in English ), a revised and substantially abbreviated version (eleven pages in English) published in 1930, and a brief abstract based on a presentation of Godel's results in Konigsberg on 6 September 1930. Of all of Godel's longer, published writings, his dissertation has been, until now, the most difficult to obtain, and is here translated for the first time into English, by Stefan Bauer-Mengelberg and van Heijenoort.
- 3 $\begingroup$ The original version of his thesis seems to have 33 pages; see permalink.obvsg.at/AC05181322 (the number next to "Umfangsangabe") $\endgroup$ – user9072 Commented Feb 8, 2011 at 16:59
- 2 $\begingroup$ I cannot say anything about the original version (my German skills are null, not almost null). But I have just checked my copy of the Collected Works (unfortunately I have not found any online library to link), and in pages 60-101 we can find Godel's dissertation (even pages match German, while odd ones match English). Thus, the description "21 pages in English" is accurate. $\endgroup$ – boumol Commented Feb 8, 2011 at 17:14
- 1 $\begingroup$ I did not want to imply your claim was not accurate. Only, as I understand the question, it is about the actual document the person submitted as a thesis. Thus, I supplemented this information, documenting it by the link to the entry of Goedels thesis in the joint library catalogue of Austrian (academic) libraries. It specifies title, author, year, lengths (that's the Umfangsangabe, S. abbreviates 'Seiten' i.e. pages), the type of document (thesis of University of Vienna (Wien)), and finally the specific libraries where it can be found. $\endgroup$ – user9072 Commented Feb 8, 2011 at 17:48
According to mathscinet, Eva Kallin's thesis was 14 pages.
- 3 $\begingroup$ This is promising, but as the question mentions and the meta thread shows, MathSciNet alone is not an authoritative reference. More documentation? $\endgroup$ – Peter LeFanu Lumsdaine Commented Feb 8, 2011 at 20:12
Barry Mazur's thesis on the proof of the Schoenflies conjecture (and introducing the method of infinite repetition in topology) is 5 pages long.
- 4 $\begingroup$ According to "Mathematical apocrypha redux" by Krantz, Mazur's thesis was 26 pages long. $\endgroup$ – Michael Greinecker Commented Feb 8, 2011 at 16:22
- 2 $\begingroup$ Mathscinet says his thesis is 30 pages. $\endgroup$ – Jaikrishnan Commented Feb 8, 2011 at 16:26
- 70 $\begingroup$ Well, it may not be the shortest but it surelyt appears to have the most variable number of pages! $\endgroup$ – Mariano Suárez-Álvarez Commented Feb 8, 2011 at 16:42
- 17 $\begingroup$ Let's please heed Timothy's call to do one's homework carefully. "Don't post a candidate unless you're sure your facts are correct, and please give some indication why you're so sure. Read the meta discussion before posting." $\endgroup$ – Todd Trimble Commented Feb 8, 2011 at 16:47
- $\begingroup$ Yikes. I had never looked at the thesis, but just the published version in the Bulletin of the AMS which is 5 pages long. $\endgroup$ – Victor Miller Commented Feb 23, 2011 at 22:12
Not the answer you're looking for? Browse other questions tagged ho.history-overview or ask your own question .
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John Nash’s Super Short PhD Thesis: 26 Pages & 2 Citations
in Math | July 9th, 2018 2 Comments
When John Nash wrote “Non Cooperative Games,” his Ph.D. dissertation at Princeton in 1950, the text of his thesis ( read it online ) was brief. It ran only 26 pages. And more particularly, it was light on citations. Nash’s diss cited two texts: John von Neumann & Oskar Morgenstern’s Theory of Games and Economic Behavior (1944), which essentially created game theory and revolutionized the field of economics; the other cited text, “Equilibrium Points in n‑Person Games,” was an article written by Nash himself. And it laid the foundation for his dissertation, another seminal work in the development of game theory, for which Nash won the Nobel Prize in Economic Sciences in 1994 .
The reward of inventing a new field is having a slim bibliography.
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by OC | Permalink | Comments (2) |
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Comments (2), 2 comments so far.
Sometimes doctoral dissertations are long on footnotes and bibliography — and short on original thinking. John Nash reversed the academic trend. Reminds me of the Renaissance painter who was asked for evidence of his ability to draw. He drew a near-perfect circle on a canvas, and was accepted by the master as an apprentice.
Excellent concept and articles.…worth reading.…pl forward more reading
Thanks and regards
Dr B Vijay Sarthi
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Doctorandum
PhD: Been There, Done That...
- The World’s Shortest PhD Dissertations
“David Lee Rector’s Ph.D. Thesis is just nine pages long plus bio and bibliography, not to mention double-spaced.” [Source & Photo Credit: Ali Almossawi ]
You have probably seen thick dissertations, too heavy to lift with one hand… but have you ever thought of how short a PhD dissertation can possibly be?
Well, John Edensor Littlewood once famously inquired “ whether a dissertation of 2 lines could deserve and get a Fellowship ” – and he seems to have meant it.
Interestingly, some of the world’s shortest PhD theses / dissertations also count among the most famous ones at the same time. Here are the Top 5 we could identify:
24 pages – John F. Nash: Non-Cooperative Games (1950)
17 pages – Albert Einstein: Eine neue Bestimmung der Moleküldimensionen (1905) / A New Determination of Molecular Dimensions (1906)
16 pages – Edmund Landau: Neuer Beweis der Gleichung (1899) / New Proof of the Equation (2007)
13 pages – Burt Totaro: Milnor K-Theory is the Simplest Part of Algebraic K-Theory (1992)
9 pages – David Lee Rector: An Unstable Adams Spectral Sequence (1966)
Please drop us a line if you know any shorter dissertations than the ones above!
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So Many Papers, so Little Time
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The Shortest Papers Ever Published
This blog post is about short papers. It seems out of place writing a long introduction.
If you ever wondered about the shortest papers ever published, or you just want to take the unique opportunity to read several papers in full within one minute, this post is for you.
Math can be short
Math can be hard and tedious resulting in very long papers. The 1995 proof of Fermat’s last Theorem was 108 pages long.
But math can also be short.
Lander and Parkin’s paper about a conjecture by Euler (related to Fermat’s last Theorem), is probably the dream of everyone ever written a paper: It answers an interesting and important question, it’s correct beyond any doubt, it’s easy to understand and only two sentences long.
Is there a way to beat that? John Conway and Alexander Soifer submitted a paper in 2005 with the goal to write the shortest math paper ever.
It is only two words long and contains two distinct proofs of their problem in two figures.
The editors were a bit surprised: “The Monthly publishes exposition of mathematics at many levels, and it contains articles both long and short. Your article, however, is a bit too short to be a good Monthly article. . . A line or two of explanation would really help.”
The authors did not give up and could convince the editors: “I respectfully disagree […] What else is there to explain?” Read the full story .
Empty pages
Can you write a meaningful paper shorter than 2 words? Probably not. Still, I want to mention the following case report of severe writer’s block, which contribute important zero words to the literature:
Also the following zero-word paper (excluding the abstract) makes an important point. Originally submitted to Nature Chemistry it did not make the cut for publication. But the editors liked it so much that they covered it in their blog and their production team produced a print PDF for it. It finally appeared in 2016 in the journal “ Chemie in unserer Zeit ” (50(2), 144–145) published by Wiley. It’s a German journal but don’t worry. The empty pages should be easy to read even in German…
Short abstracts
Abstracts should be short by definition. But some are shorter than others. These are the shortest we could find:
Enough already
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Short but Substantial Math Papers [closed]
I am looking for short papers that made a significant impact on the mathematics community. I have already seen: interesting-but-short-math-papers and, What is the Shortest Ph.D. Thesis? on math overflow, but these weren't quite what I was looking for (although the intersection of the set of answers to this question with the set of answers to either of the above links is likely to be non-trivial)
I am more interested in short and important works of mathematics, not necessarily Ph.D.s (but not necessarily not Ph.D.s either). Things that changed the course of mathematical history, that sort of thing.
Any suggested readings would be very much appreciated.
I realize I was not clear on what I meant by short. around the 20 page or less mark. If it goes higher, but is really something for its size then that is acceptable too.
- reference-request
- soft-question
- math-history
- 3 $\begingroup$ A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I. $\endgroup$ – blub Commented Aug 31, 2018 at 13:14
- 3 $\begingroup$ This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above). $\endgroup$ – Arnaud D. Commented Aug 31, 2018 at 13:19
- $\begingroup$ Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit). $\endgroup$ – chepner Commented Aug 31, 2018 at 15:19
- $\begingroup$ @chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =) $\endgroup$ – user21820 Commented Aug 31, 2018 at 16:48
- 1 $\begingroup$ If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye". $\endgroup$ – Eric Duminil Commented Aug 31, 2018 at 21:40
7 Answers 7
Riemann's short paper, "Über die Anzahl der Primzahlen unter einer gegebenen Grösse," surely qualifies.
- 1 $\begingroup$ I've made this answer community wiki so that upvotes can indicate agreement rather than reward. $\endgroup$ – Barry Cipra Commented Aug 31, 2018 at 13:36
Not a paper, but definitely significant, is Russell's paradoxical letter to Frege.
- $\begingroup$ I've made this answer community wiki so that upvotes can indicate agreement rather than reward. $\endgroup$ – Barry Cipra Commented Aug 31, 2018 at 13:36
I would recommend Classics of Mathematics , ed. Ronald Calinger. It's got articles from a very broad range of mathematical history, all the way from the Stone Age through 1932 (includes Gödel). Naturally, it does not include later works. Most of the most important ideas in modern mathematics will be found in here somewhere. For more modern topics, I found Love and Math by Edward Frenkel to be excellent.
Short does not mean a lot of things for me. A paper may be short, but to understand it you may have to read a lot of books. You can read the work of Milnor, he is very well-known for is concise papers which are very well written. Look for example his work on exotic spheres.
Milnor, John W. (1959), "Differentiable structures on spheres", American Journal of Mathematics, 81 (4): 962–972
There is a proof of the non-existence of vector fields on spheres by (Adams and Atiyah ?) that was famously said, could fit on a post card. There is an Indian mathematician named C.P. Ramanujan who wrote a number of very important papers in algebraic geometry and number theory. To the best of my recollection, none of his papers is over 20 pages.
The Proceedings of the AMS is all about short papers. You could probably search MathSciNet for publications in the Proceedings and sort by citation number to find some winners.
I'd do this myself, but I don't have a login right now :c
The Noah Sheets helped me a lot in contest math.
- 1 $\begingroup$ I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae. $\endgroup$ – Arnaud D. Commented Sep 3, 2018 at 11:49
- $\begingroup$ Oh... well then I guess I can't contribute... $\endgroup$ – Jason Kim Commented Sep 3, 2018 at 16:08
Not the answer you're looking for? Browse other questions tagged reference-request soft-question math-history big-list .
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Mathematics PhD dissertations that opened a new field of research
I propose this as a companion wiki page to the one about PhD dissertations which contain a solution to an open problem in the style of big-list questions, thinking in terms of the well-known paradigm that splits mathematical research into problem solving and theory building . Theories are at times developed to solve famous open problems, but sometimes the concrete problems they solve are quickly dwarfed by the possibilities that a new theory opens.
Can you name modern mathematicians who already in their PhD theses (or earlier in their career) developed a substantial new theory or laid the foundations of a new field of research?
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- 9 $\begingroup$ The list will be too long. $\endgroup$ – Alexandre Eremenko Commented Apr 24, 2018 at 12:11
- 6 $\begingroup$ en.wikipedia.org/wiki/Tate%27s_thesis $\endgroup$ – Steve Huntsman Commented Apr 24, 2018 at 12:14
- 2 $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$ – Steve Huntsman Commented Apr 24, 2018 at 12:15
- 2 $\begingroup$ Perhaps Scholze's Perfectoid spaces ? $\endgroup$ – TKe Commented Apr 24, 2018 at 14:25
- 2 $\begingroup$ @Steve Huntsman: Shannon's thesis does not qualify: it was a master thesis:-) $\endgroup$ – Alexandre Eremenko Commented Apr 25, 2018 at 2:52
5 Answers 5
John Forbes Nash Jr. got a Nobel Prize for his.
Nash earned a Ph.D. degree in 1950 with a 28-page dissertation on non-cooperative games. The thesis, written under the supervision of doctoral advisor Albert W. Tucker, contained the definition and properties of the Nash equilibrium, a crucial concept in non-cooperative games. It won Nash the Nobel Memorial Prize in Economic Sciences in 1994.
There are many examples. Here are a few that come to mind:
Simon Donaldson's thesis The Yang-Mills equations on Kahler manifolds contains the first major steps in his work on the differential topology of four manifolds. The following paraphrases its abstract. He gave a new proof of a theorem of Narasimhan and Seshadri characterizing those holomorphic bundles over a projective curve that admit a flat connection and used it to prove the simplest interesting case of the conjecture of Hitchin and Kobayashi. He studied the moduli space of self-dual connections on a simply-connected four manifold and used it to deduce obstructions to the realization of a matrix as the intersection pairing on the second cohomology of such a manifold.
John Tate's thesis is another well known example, although I'm not competent even to summarize it. It has its own wikipedia page .
Mikio Sato's doctoral thesis (based on some already published work) introduced the theory of hyperfunctions as boundary values of holomorphic functions. See this survey by P. Schapira and this interview with Sato. (Nothing about Sato's education is standard.)
- $\begingroup$ I read that article my Mikio Sato. I thought it very interesting. Too bad most famous mathematicians seem to be as unforthcoming as Sato in describing their formative influences. $\endgroup$ – Mozibur Ullah Commented May 3, 2018 at 4:51
I’ll pick Philippe Delsarte’s 1973 thesis “An algebraic approach to the association schemes of coding theory” which basically expressed classical extremal problems in designs and codes as algebraic questions involving eigenspaces of related association schemes.
Here is a link to a talk on what is now known as “ Delsarte Theory ”.
Maybe not up to the Nash standard, but pretty good for a PhD!
Thomas G. Kurtz ' PhD dissertation at Stanford University (1967) was titled Convergence of operator semigroups with applications to Markov processes . He went on to write with his PhD student Stewart N. Ethier the book Markov Processes: Characterization and Convergence (John Wiley & Sons Inc., 1986), which is "the standard reference for the advanced theory of Markov processes". Its first chapter is Operator semigroups . He made a stellar research career on these foundations. Much of the modern theory of stochastic processes is variations of what he pioneered: "establishing the convergence of Markov processes and characterising the limiting process" (quotes from the Wikipedia page). I do not claim that he single-handedly created the area, but his contribution is immense.
There has been a similar question here: https://www.quora.com/Which-are-the-best-PhD-theses-ever-in-pure-mathematics
I would suggest Kurt Godel. His doctorate thesis proved the completeness theorem, and a year later he published his incompleteness theorems.
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The Dramatic and Ultimate Shortening of a Doctoral Dissertation in Mathematics
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Length of the average dissertation
On R is My Friend, as a way to procrastinate on his own dissertation, beckmw took a look at dissertation length via the digital archives at the University of Minnesota.
I’ve selected the top fifty majors with the highest number of dissertations and created boxplots to show relative distributions. Not many differences are observed among the majors, although some exceptions are apparent. Economics, mathematics, and biostatistics had the lowest median page lengths, whereas anthropology, history, and political science had the highest median page lengths. This distinction makes sense given the nature of the disciplines.
I was on the long end of the statistics distribution, around 180 pages. Probably because I had a lot of pictures.
As I was working on my dissertation, people often asked me how many pages I had written and how many pages I had left to write. I never had a good answer, because there’s no page limit or required page count. It’s just whenever you (and your adviser) feel like there’s enough to get a point across. Sometimes that takes 50 pages. Other times it takes 200.
So for those who get that dreaded page-count question, you can wave your finger at this chart and tell people you’re somewhere in the distribution.
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13 Comments
As a student at Minnesota, I’m not sure our digital archive is representative, as it is optional, and and certain fields are more or less likely (either due to subject matter, or internal politics) to include their works within the archive. Other than that, this is neat!
what do the colors mean? at first glance I thought the colors had to do with subject area, but on closer examination that are same colored major that are very different (i.e. anthropology/aerospace engineering,
The colors look like they are reverse alphabetical.
Kyle, thanks – I figured I was missing something super simple – its been a long day. So the colors are meaningless then?
Yes, the colors are useless. They convey no information that is not already transparently conveyed.
For that matter, the box plot itself is thoroughly obsolete. Read Edward Tufte’s books, specifically chapter 6 of “The Visual Display of Quantitative Information” for the description of the successor to the box plot.
As for the topic of the post, my math dissertation was 88 pages. My advisor’s was (not a typo) 23 pages, double-spaced, including front matter and references.
And Presburger’s was 19 pages or so. But his supervisor, Tarski, would not give him his PhD. He thought the thesis was too short. So there is a lower bound.
would be interesting to see if they have been getting longer over time and by how much by subject
The chart would be more useful if the majors were ordered by median or average dissertatin length. But it is interesting to note that the more mathematical and objective the mayor, the less pages needed. Llongest dissertations: sociology and anthropology. Shortest: biostatistics.
Out of curiosity, Nathan, what was your dissertation on? (Not that I’d understand it anyway!)
Then, there are the departments’ or universities’ format standards. Single spaced? Double spaced? That, of course doubles the plage length. Better, what was the word count in the dissertations?
So with the current trend of dissertation chapters being prepared/formatted as manuscript submissions for journals up front (which have limits to the manuscript length), I would expect to see overall dissertation lengths get shorter over time (to present). Mine started out much longer, but as I started conforming to target journal format standards, I would say the overall length was reduced by a third or so. Is this true outside of ecology as well?
Oh, dear, my dissertation wouldn’t even appear on this chart, but would be off the right edge. And yes, I’m in one of the ‘runs long’ disciplines. Then again, my opus would count as short for, say, a German Habilitation or a French These d’Etat in my field, so it all depends!
This is very interesting. One variable that isn’t accounted for, but varies greatly between institutions and individual authors, is the number of words per page – determined by spacing, margins, font size, and so on. A more helpful plot would count theses by words, instead of pages, as a measure of content.
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Below is a list of PhD dissertations written by students at the Harvard Department of Mathematics. All scholars can order copies of most Harvard dissertations from 1982 to the present by contacting UMI/ProQuest at 1-800-521-3042. Permission of the author is usually required to copy theses within the last five years. Most PhD dissertations submitted from March 2012 forward are available online in Harvard's central open-access repository. Harvard affiliates with IDs and PINs can access the full text of most Harvard PhD theses since 1990 from the . of the Harvard Mathematics department. |
Year | Name | Advisor | Title |
2019 | Mark Kisin | Slopes in eigenvarieties for definite unitary groups | |
2019 | Michael Hopkins | Real Orientations of Lubin-Tate Spectra and the Slice Spectral Sequence of a C4-Equivariant Height-4 Theory | |
2019 | Mark Kisin | The p-curvature conjecture for the non-abelian Gauss-Manin connection | |
2019 | Curtis McMullen | Trees, Berkovich spaces and the barycentric extension in complex dynamics | |
2019 | Horng-Tzer Yau | Spectral Statistics of Random d-regular Graphs | |
2019 | Barry Mazur | Ramification of the Hilbert Eigenvariety | |
2019 | Joe Harris | Stable log surfaces, trigonal covers, and canonical curves of genus 4 | |
2019 | Hugh Woodin | The Ultrapower Axiom | |
2019 | Martin Nowak | Indirect Reciprocity with Optional Interactions and Private Information and Stochastic Evolution of Staying Together. | |
2019 | Shing-Tung Yau | Mirror Symmetry, Autoequivalences, and Bridgeland Stability Conditions | |
2018 | Minicozzi | Geometric Variational Problems for Mean Curvature | |
2018 | Taubes | Several compactness results in gauge theory and low dimensional topology | |
2018 | S-T Yau | Picard-Fuchs systems arising from toric and flag varieties | |
2018 | S-T Yau | Entire surfaces of prescribed curvature in Minkowski 3-space | |
2018 | Kisin | Geometric Properties of Families of Galois Representations | |
2018 | H-T Yau | Local statistics of Dyson Brownian motion | |
2018 | M. Hopkins | Variations on a Nilpotence Theorem of Hopkins and Mahowald | |
2018 | M.Hopkins | Some calculations of cobordism groups and their applications in physics | |
2018 | Curtis McMullen | Teichmüller curves in genus two: square-tiled surfaces and modular curves | |
2018 | H.T. Yau | Universality of random matrices with dependent entries | |
2018 | Dennis Gaitsgory | Nearby cycles of Whittaker sheaves | |
2017 | Mark Kisin | The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties | |
2017 | Mark Kisin | Mod-p isogeny classes on Shimura varieties with parahoric level structure | |
2017 | Mark Kisin | The p-curvature conjecture and monodromy about simple closed loops | |
2017 | Michael Hopkins | Symmetric Powers and the Equivariant Dual Steenrod Algebra | |
2017 | Jacob Lurie | Nilpotence and descent in stable homotopy theory | |
2017 | Mark Kisin | Integral canonical models for G-bundles on Shimura varieties of abelian type | |
2017 | Mark Kisin | A p-adic Jacquet-Langlands Correspondence | |
2017 | Jacob Lurie | The Lubin-Tate Theory of Spectral Lie Algebras | |
2016 | Joe Harris | Degenerations, Log K3 Pairs and Low Genus Curves on Algebraic Varieties | |
2016 | Peter Kronheimer | On the Framed Singular Instanton Floer Homology from Higher Rank Bundles | |
2016 | Michael Hopkins | Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds | |
2016 | Mark Kisin | Algebraicity criteria and their applications | |
2016 | Joe Harris | Derived categories and birational geometry of Gushel-Mukai varieties | |
2016 | Mark Kisin | Galois Deformation Ring and Barsotti-Tate Representations in the Relative Case | |
2016 | Alexei Borodin (MIT) | q-deformed Interacting Particle Systems, RSKs and Random Polymers | |
2016 | Benedict Gross | On the Moy-Prasad filtration and stable vectors | |
2016 | Joe Harris | Complete Homogeneous Varieties via Representation Theory | |
2016 | Benedict Gross | On the Arithmetic of Hyperelliptic Curves | |
2015 | Dick Gross | A formula for some Shalika germs | |
2015 | Clifford Taubes | The moduli space of S1-Type zero loci for Z/2 Harmonic spinors in dimension 3 | |
2015 | Michael Hopkins | Structures on Forms of K-Theory | |
2015 | Dennis Gaitsgory | Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification | |
2015 | Joe Harris | Rational Curves on Hypersurfaces | |
2015 | Dick Gross | 2-Selmer groups and Heegner points on eliptic curves | |
2015 | Alexei Borodin | Several Theorems about Probabilistic limiting Expressions: The Gaussian free field, symmetric Pearcey process, and strong Szegö asymptotics | |
2015 | Jacob Lurie | Goodwillie approximations to higher categories | |
2015 | Joe Harris | Covers of an elliptic curve E and curves in E x P1 | |
2015 | Richard Taylor | Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations | |
2015 | Joe Harris | Interpolation and vector bundles on curves | |
2015 | Jacob Lurie | The mod 2 homology of free spectral Lie algebras | |
2014 | S.T Yau | Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds | |
2014 | Joe Harris | Relative Jacobeans of Linear Systems | |
2014 | Dennis Gatisgory | Chiral Principal Series Categories | |
2014 | Joe Harris | Regeneration of Elliptic Chains with Exceptional Linear Series | |
2014 | RIchard Taylor | Modularity of some elliptic curves over totally real fields | |
2014 | Curt McMullen | The geometry of the Weil-Petersson metric in complex dynamics | |
2014 | Marc Kisin | The Eigencurve is Proper | |
2014 | Peter Kronheimer | Symmetric Spaces and Knot Invariants from Gauge Theory | |
2014 | Curtis McMullen | The complex geometry of Teichmuller space | |
2013 | Joe Harris | Pencils of quadrics and Jacobians of hyperellipitc curves | |
2013 | Benedict Gross | Moduli of Galois Representations | |
2013 | Benedict Gross | On Newforms for Split Special Odd Orthogonal Groups | |
2013 | Curt McMullen | Entropy, dimension and combinatorial moduli for one-dimensional dynamical systems | |
2013 | Yum-Tong Siu | Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications | |
2013 | Joe Harris | The Geometry of Hurwitz Space | |
2013 | Shing-Tung Yau | Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing | |
2013 | Noam Elkies | Rational Point Counts for del Pezzo Surfaces over Finite Fields and Coding Theory | |
2012 | Richard Taylor | The Arithmetic of Simple Singularities | |
2012 | Peter Kronheimer | Towards an Instanton Floer Homology for Tangles | |
2012 | Florian Pop | Anabelian Intersection Theory | |
2012 | Shing-Tung Yau | Analysis of some PDEs over manifolds | |
2012 | Curtis McMullen | Mapping class groups, homology and finite covers of surfaces | |
2012 | Peter Kronheimer | Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls | |
2012 | Joe Harris | Restrictions of Steiner bundles and divisors on the Hilbert scheme of points in the plane | |
2012 | Joe Harris | Alternate Compactifications of Hurwitz spaces | |
2012 | Richard Taylor | Local-Global Compatibility and the Action of Monodromy on Nearby Cycles | |
2012 | Martin Nowak | Mathematical Models of Cancer | |
2012 | Dennis Gaitsgory | D-modules on Spaces of Rational Maps and on Other Generic Data | |
2011 | Pavel Etingof | Representations of the rational Cherednik algebras | |
2011 | Clifford Taubes | Asymptotic spectral flow for Dirac operators of disjoint Dehn twists | |
2011 | Shing-Tung Yau | The Picard-Fuchs systems of Calabi-Yau complete intersections in homogeneous spaces | |
2011 | Dick Gross | The Local Langlands Correspondence for Tamely Ramified Groups | |
2011 | Dennis Gaitsgory | Twisted geometric Satake equivalence via gerbes on the factorizable grassmannian | |
2011 | Richard Stanley | Combinatorial applications of symmetric function theory to certain classes of permutations and truncated tableaux | |
2011 | Shing-Tung Yau | Calabi-Yau Geometry and Higer Genus Mirror Symmetry | |
2011 | Barry Mazur | On Elliptic Curves, the ABC Conjecture, and Polynomial Threshold Functions | |
2011 | Richard Taylor | The Picard-Fuchs systems of Calabi-Yau complete intersections in homogeneous spaces | |
2011 | Shing Tung Yau | Existence of Hermitian-Yang-Mills Metrics under Conifold Transitions | |
2011 | Shing-Tung Yau | Quasi-local energy in General Relativity | |
2010 | Noam Elkies | K3 surfaces of high Picard number and arithmetic applications | |
2010 | Noam Elkies | Arithmetic of Elliptic Curves and Surface: Descents and Quadratic Sections | |
2010 | Joseph Harris | Moduli of singular curves and crimping | |
2010 | Denis Auroux (MIT) | A monoidal structure for the Fukaya category | |
2010 | Horng-Tzer Yau | Lower Bound for Ground State Energy of Dilute Bose Gas | |
2010 | Noam Elkies | Some combinatorial problems in vector spaces over finite fields | |
2010 | Richard Taylor | Modularity Lifting Theorems for Ordinary Galois Representations | |
2009 | Shing-Tung Yau | Geometry of complex Monge-Ampère equations | |
2009 | Martin Nowak | Evolutionary Dynamics in Structured Populations | |
2009 | Richard Stanley | Enumeration of the Distinct Shuffles of Permutations | |
2009 | Cliff Taubes | A Number Theoretic Result for Berge's Conjecture | |
2009 | Joe Harris | Good Completions of Neron Models | |
2009 | Michael Hopkins | Cubical Homotopy Theory and Monoidal Model Categories | |
2009 | Michael Hopkins | A generalization of a theorem of Ravenel and Wilson | |
2009 | Barry Mazur | Filament Geometry | |
2009 | Richard Taylor | Local Universal Deformation Lifting Spaces Of Mod L Galois Representations | |
2009 | Shing-Tung Yau | Pseudonorms and Theorems of Torelli Type for Birational Equivalence | |
2009 | Joe Harris | Subcanonical Points on Algebraic | |
2009 | Michael Hopkins | A Structures on Thom Spectra | |
2009 | Richard Taylor | On Potential Automorphy and other topics in Number Theory | |
2008 | Joe Harris | Compact Moduli of Singular Curves: A Case Study in Genus One | |
2008 | Barry Mazur | Selmer Growth and a Triangulordinary Local Condition | |
2008 | Richard Taylor | Arithmetic Compactifications of PEL-type Shimura Varieties | |
2008 | Barry Mazur | Algorithms for p-adic Cohomology and p-adic Heights | |
2008 | Gerald Sacks | Models with High Scott Rank | |
2008 | Joe Harris | Severi Varieties and the Moduli Space of Curves | |
2008 | Joe Harris | Covers of Elliptic Curves and Slopes of Effective Divisors on the Moduli Space of Curves | |
2008 | Roman Bezrukavnikov (MIT) | Weak Representation of Tangle Categories in Algebraic Geometry | |
2008 | Cliff Taubes | Investigation of J-holomorphic curves in M3 x S1 | |
2007 | Richard Taylor | Counting points on Igusa varieties | |
2007 | Martin Nowak | Modeling the Effects of Population Structure and Vaccination Strategy on Infectious Diseases | |
2007 | Barry Mazur | The Exceptional Zero Conjecture For Hilbert Modular Form | |
2007 | Peter Kronheimer | A slice genus lower bound from sl(n) Khovanov-Rozansky homology | |
2007 | Noam Elkies | Minimal Heights and Regulators for Elliptic Surfaces | |
2007 | Joe Harris | Enumerative Geometry of Curves with Exceptional Secant Planes | |
2006 | Shing-Tung Yau | On Ordinary K3 surfaces over F | |
2006 | Richard Taylor | Weight Spectral Sequence and Hecke Correspondence on Shimura Varieties | |
2006 | Shing-Tung Yau | On the Geometry of Superstring with Torsion | |
2006 | Peter Kronheimer | Estimated Transversality And Rational Maps | |
2006 | Richard Taylor | Weights Of Galois Representations Associated To Hilbert Modular Forms | |
2006 | Joe Harris | On Zero-Dimensional Schemes with Special Hilbert Functions | |
2006 | Martin Nowak | Analysis of Probabilistic Models of Evolution | |
2006 | Noam Elkies | K3 surfaces of high rank | |
2006 | Richard Taylor | The Weight in Serre Type Conjecture for Tame n-Dimensional Galois Representations | |
2006 | Wilfried Schmid | The Degree 4 L-Function of an Automorphic Form of Full Level on the Rank 2 Real Symplectic Group | |
2006 | Joe Harris | Extending Families of Curves: Monodromy and Applications | |
2006 | Curtis McMullen | Euler Characteristics of Teichm?ller Curves in Genus Two | |
2005 | Cliff Taubes | Applications of Chiral Perturbation Theory | |
2005 | Cliff Taubes | Pseudoholomorphic Punctured Spheres in the Symplectization of a Quotient | |
2005 | Shing-Tung Yau | A Modular Non-Rigid Calabi-Yau Threefold | |
2005 | Joe Harris | Moduli Spaces of Curves with Linear Series and the Slope Conjecture | |
2005 | Shlomo Sternberg | Morphlets; A Multiscale Representation for Diffeomorphisms | |
2005 | Richard Taylor | Kato's Euler System and the Main Conjecture | |
2005 | Richard Taylor | Geometricity of Local p-Adic Representations | |
2004 | Joe Harris | Special Linear Series in P2 | |
2004 | Noam Elkies | Elliptic Curves x + y = k with High Rank | |
2004 | Cliff Taubes | Perturbations of the D-bar Operator | |
2004 | Barry Mazur | Geometric and p-Adic Modular Forms of Half-Integral Weight | |
2004 | Peter Kronheimer | Contact Structures and Floer Homology | |
2004 | Curtis McMullen | Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves | |
2004 | Shing-Tung Yau | Intersection Theory on the Moduli Space of Stable Bundles via Morphism Spaces | |
2004 | Peter Kronheimer | A Spectrum Valued RQFT from the Seiberg-Witten Equations | |
2004 | Curtis McMullen | Complex Projective Structures | |
2004 | Joe Harris | Degenerations of scrolls and Del Pezzo Surfaces and Applications to Enumerative Geometry | |
2003 | Benedict Gross | The Fourier-Jacobi map and small representations | |
2003 | Peter Kronheimer | Floer Homology and Knot Complements | |
2003 | Benedict Gross | Central value of Rankin L-series over real quadratic fields | |
2003 | Benedict Gross | Quaternion Rings | |
2003 | Barry Mazur | Generalization of the Turan and the Erdos-Kac Theorems | |
2003 | Shing-Tung Yau | Deformations of G and Spin(7) Structures on Manifolds | |
2003 | Noam Elkies | Supersingular primes for rational points on modular curves | |
2003 | Barry Mazur | Local and global points on moduli spaces of abelian surfaces with potential quaternionic multiplication | |
2003 | Shing-Tung Yau | Li-Yau-Hamilton Estimate for the Ricci Flow | |
2003 | Shing-Tung Yau | Flops and Equivalences of derived Categories for Threefolds with only terminal Gorenstein Singularities | |
2002 | Benedict Gross | Hecke Algebra action on Siegel Modular Forms | |
2002 | Barry Mazur | On u-Invariants of Elliptic Curves over Q | |
2002 | Cliff Taubes | Closed Self-Dual Two-Forms on Four-Dimensional Handlebodies | |
2002 | Richard Taylor | On Certain Unitary Group Shimura Varieties | |
2002 | Shing-Tung Yau | Moduli of J-Holomorphic Curves with Lagrangian Boundry Conditions | |
2002 | Wilfried Schmid | A Localization Argument for Characters of Reductive Lie Groups | |
2002 | Yum-Tong Siu | Effective Schottky problem | |
2002 | Curtis McMullen | Holomorphic families of Rational Maps: Dynamics Geometry and Potential Theory | |
2002 | David Kazhdan | Fourier Transform for Quantized Completely Integrable Systems | |
2001 | David Kazhdan | Hodge Structure on the Fundemental Group and its Application to p-adic Integrarion | |
2001 | Richard Taylor | Modularity of some potentially Barsotti-Tate Galois representations | |
2001 | Barry Mazur | On the p-adic L-function of a Modular Form at a Supersingular Prime | |
2001 | Richard Taylor | Local Level-Raising for GL | |
2001 | Barry Mazur | Modular Varieties and Visibility | |
2000 | Shing-Tung Yau | The Global Nonlinear Stability of the Trivial Solution of the Einstein-Maxwell Equations | |
2000 | Barry Mazur | On Selmer groups of geometric Galois Representations | |
2000 | Shing-Tung Yau | Compact Manifolds with Exceptional Holonomy | |
2000 | Joe Harris | Rational Curves on Hypersurfaces in Pn | |
2000 | Shlomo Sternberg | Symmetric Space Valued Moment Maps | |
2000 | Peter Kronheimer | PU(2) monopoles on Kahler surfaces | |
2000 | Richard Taylor | On the Modularity of Certain 2-adic Galois Representations | |
2000 | Noam Elkies | New Bounds on Sphere Packings | |
2000 | Raoul Bott | Equivariant de Rham Theory and Statinary Phase Expansions | |
1999 | Joe Harris | Exact Rates of Convergence for Some Simple Non-Reversible Markocv Chains | |
1999 | Cliff Taubes | Configuration space and Monopoles for Yang-Mills-Higgs Theory on R /M | |
1999 | Barry Mazur | Flat Regular Models of Elliptic Schemes | |
1999 | Joe Harris | Monomial Ideals and Hilbert Schemes | |
1999 | Barry Mazur | Jacobians of Curves of Genus One | |
1999 | Joe Harris | Moduli Spaces of Curves with Marked Points | |
1999 | Shing-Tung Yau | Applications of Affine Differential Geometry to RP(2) Surfaces | |
1999 | Cliff Taubes | Dirac Operators on Loop Spaces | |
1999 | Benedict Gross | Models over Z for Locally Quasi-Split Algebraic Groups | |
1999 | Shing-Tung Yau | Picard-Fuchs Uniformation and Geometric Isomonodromic Deformations | |
1999 | Joe Harris | Moduli of curves with level structure | |
1999 | Edward Frenkel | Spectral Curves | |
1998 | Richard Melrose (MIT) | Microlocal Analysis of the Time-Dependent Schroedinger Operator | |
1998 | Persi Diaconis | Eigenvalue Distribution of Random Matrices in Permutation Group and Compact Lie Groups | |
1998 | Shing-Tung Yau | Generalized Harmonic Maps and Representations of Discrete Groups | |
1998 | Shing-Tung Yau | Topology of Birational Manifolds and Applications to Degeneration | |
1998 | David Mumford | Curvature Motions, Medial Axes and Distance Transforms | |
1998 | Joe Harris | Calculations on the Moduli Space of Genus Zero Covers | |
1998 | Koszul Property and Bogomolov's Conjecture | ||
1998 | Benedict Gross | Explicit Hecke Actions on Modular Forms | |
1998 | Benedict Gross | Traces of Hecke Operators | |
1998 | Joe Harris | Moduli Space of Enriched Stable Curves | |
1998 | Benedict Gross | Hecke rings of Groups over Local Fields | |
1998 | Cliff Taubes | Reidemeister Torsion in Generalized Morse Theory | |
1998 | Benedict Gross | Spin Representations and Lattices | |
1998 | Benedict Gross | Exceptional Theta Correspondences | |
1998 | Barry Mazur | 2-adic Modular Forms of Minimal Slope | |
1998 | Barry Mazur | Hilbert Modular Forms and the Galois Representations Associated to Hilbert-Blumenthal Abelian Varieties | |
1998 | Benedict Gross | Variation of capacity for Convex Domains in Euclidean Space | |
1997 | David Kazhdan | Integral Motives of Quadrics | |
1997 | Joe Harris | Enumerative Geometry of Curves via Degeneration Methods | |
1997 | David Kazhdan | Short Time Behavior of Logarithmic Derivatives of the Heat Kernel | |
1997 | Joe Harris | Moduli of Trigonal Curves | |
1997 | Ehud Hrushovski | Model Theory of Valued D-Fields | |
1997 | Persi Diaconis | Random Walks on Groups: Strong Uniform Time Approach | |
1997 | Benedict Gross | Abelian L-Functions Twisted by Algebraic Tori A+S=0 | |
1997 | Benedict Gross | Exceptional Lie Groups and Lie Algebras | |
1997 | Robert MacPherson | A Generalization of Springer Theory using Nearby Cycles | |
1997 | Persi Diaconis | Probability in the Classical Groups over Finite Fields: Symmetric Functions Stochastic Algorithms and Cycle Indices | |
1997 | Benedict Gross | p-adic Gamma Functions | |
1997 | Joe Harris | Rational Curves of K3 Surfaces | |
1996 | Persi Diaconis | Socks and Boxes: Variations on Daniel Bernoulli's Marriage Problem | |
1996 | Persi Diaconis | Weighted Poincare and Exhaustive Techniques for Scaled Metropolis-Hastings Algorithms and Spectral total Variation Convergence Bounds in Infinite Commutable Markov Chain Theory | |
1996 | David Kazhdan | Biextension Weil Representations on Derived Categories and Theta Functions | |
1996 | Persi Diaconis | Berry-Essen Central Limit Theorem for Markov Chains | |
1996 | Persi Diaconis | Random Walks on the Symmetric Group Generated by Conjugacy Classes | |
1996 | Shing-Tung Yau | Wall Crossing Formula of Seiberg-Witten Invariants and Symplectic Four Manifolds with b+1=1 | |
1996 | Joe Harris | Special Cubic Hypersurfaces of Dimension Four | |
1995 | David Kazhdan | Cohomology of compact Hyperkaehler Manifolds | |
1995 | Persi Diaconis | Methods for Quantifying Rates of Convergence for Random Walks on Groups | |
1995 | Joe Harris | The Grothendieck Quot Schemes and Composition Laws for Grassmannians | |
1995 | David Kazhdan | Minimal Representations of Exceptional p-adic groups | |
1995 | Shing-Tung Yau | On the Convergence of Kahler Metrics | |
1995 | Persi Diaconis | Topics in Probability on Compact Lie Groups | |
1995 | Persi Diaconis | Walks and Representation Theory | |
1995 | Cliff Taubes | A Mayer-Vietoris Principle for Monopoles | |
1994 | Benedict Gross | A-divisible Modules | |
1994 | Barry Mazur | Canonical Heights and Rational Points on Varieties with Many Elliptic Fibrations | |
1994 | Wilfried Schmid | Real Forms of Quantum Groups and Harish-Chandra Modules | |
1994 | Raoul Bott | Lie Algebra Cohomology and the Fusion Rules | |
1994 | Joe Harris | A Compactification over the Moduli space of Stable curves of the Universal Moduli Space pf Slope-Semistable Vector Bundles | |
1994 | Joe Harris | The Moduli Space of (3,3,3) Trilinear Forms | |
1994 | Benedict Gross | Multiplicities in restricted Representations of GL (F ) U (F ) and SO(F ) | |
1994 | Joseph Bernstein | Fusion Categories | |
1994 | Raoul Bott | Some explicit Cocycles for Cohomology Classes of Groups of Diffeomorphisms Preserving a G-Structure | |
1994 | Cliff Taubes | Symplectic Geometry and the Relative Donaldson Invariants of the Conjugate Projective Plan | |
1994 | Yum-Tong Siu | An Effective Polynomial Bound for Base Point Freeness and Point Separation of Adjoint Bundles | |
1993 | Cliff Taubes | Essays on Vortices Knots and Monopoles | |
1993 | Raoul Bott | Group Actions and Cohomology | |
1993 | David Kazhdan | Graded Lie Algebras and conformal Field theories l: The Genus O Case | |
1993 | Persi Diaconis | Fast Transforms and Sampling for Compact groups | |
1993 | J. Bernstein | Formulas for Generalized Kazhdan-Lusztig Polynomials | |
1993 | Shing-Tung Yau | On Modular Invariants and Rigidity Theorems | |
1993 | Shlomo Sternberg | Hamiltonian Actions of Lie Groups | |
1993 | Yum-Tong Siu | Global Nondeformability of the Complex Hyperquadric | |
1993 | Cliff Taubes | On the ends of the monopole Moduli Space | |
1993 | Benedict Gross | The 2nd Descent for Certain Families of Mordell-Weil Lattices | |
1993 | Victor Kac | Differentiably Simple Lie Superalgebras | |
1993 | Joe Harris | On a Compactification of the Universal Picard variety over the Moduli space of Stable Curves | |
1993 | Persi Diaconis | Rates of Convergence of Markov Chains Related to Association Schemes | |
1992 | Wilfried Schmid | Dolbeault Cohomologies and Zuckerman Modules Associated with Finite Rank Representations | |
1992 | Raoul Bott | Extension of Self-Dual Yang-Mills Equations across the Eight Dimension | |
1992 | Barry Mazur | Higher-Order Characteristic Classes in Arithmetic Geometry | |
1992 | David Kazhdan | Homology of Schemes and covariant Motives | |
1992 | Raoul Bott | The Verlinde Formulas and Moduli Spaces of Vector Bundles | |
1992 | Heisuke Hironaka | Functional Smoothing of Morphisms in Equal Characteristic 0 | |
1992 | Persi Diaconis | Rates of Convergence for Gibbs Sampler and other Markov Chains | |
1992 | Barry Mazur | Division Points on Semi-Abelian Varieties | |
1992 | Benedict Gross | A p-adic Computation of Singular Moduli | |
1992 | Joe Harris | Hilbert and Functions of Zero-Dimensional Schemes in Uniform Position | |
1992 | Joe Harris | On the Dimension of the Chow Varieties | |
1991 | Cliff Taubes | Yang-Mills Connections with Asymptotically Constant Curvature | |
1991 | Barry Mazur | Power-free Values of Polynomials | |
1991 | Joe Harris | On the Hyperplane sections of a Variety in Projective Space | |
1991 | Joseph Bernstein | Affine Kac-Moody Algebras at the Critical Level and Quantum Drinfield-Sokolov Reduction | |
1991 | Benedict Gross | Refined Class Formulas for Derivatives of L-Series | |
1991 | Barry Mazur | Weierstrass Points on Arithmetic Surfaces | |
1991 | Barry Mazur | An Arithmetic Riemann-Roch Theorem for Singular Arithmetic Surfaces | |
1991 | Joe Harris | Subvarieties of Abelian Varieties and of Jacobians of Curves | |
1990 | David Mumford | Image Segmentation by Variational Methods and Elliptic Boundary Value Problems | |
1990 | John Tate | Refined Conjectures of the Birch and Swinnerton-Dyer Type | |
1990 | Cliff Taubes | Nonexistence of Almost Handebody Structures on Topological Four Manifold Pairs | |
1990 | Joseph Bernstein | Deligne's Conjecture in the Constant Coefficient Case | |
1990 | Shing-Tung Yau | Ricci Deformation of the Metric on Complete Noncompact Kahler Manifolds | |
1990 | Barry Mazur | Igusa Towers over Hilbert Modular Surfaces | |
1990 | Mark Spivakovsky | On Some Conditions of Regularity for Subanalytic Sets | |
1990 | Shing-Tung Yau | On Meromorthic Maps between Algebraic Varieties with Log-General Targets | |
1990 | Shing-Tung Yau | Construction of Stable Vector Bundle on Surface of Low 2nd Chern Classification | |
1990 | Joe Harris | Divisors on Some Moduli Spaces | |
1990 | Persi Diaconis | Rates of Convergence of Some Random Processes on Finite Groups | |
1990 | John Tate | Spaces of Rational Functions on Curves over Finite Fields | |
1989 | Shing-Tung Yau | Semipositive Threefolds and Threefolds with Universal covering C(3) | |
1989 | Persi Diaconis | Fast Fourier Analysis for Finite Groups | |
1989 | Benedict Gross | Shimura Curves Analogous to X (N) | |
1989 | Benedict Gross | Trilinear Forms for GL (2) of a Local Field and Epsilon Factors | |
1989 | Raoul Bott | Hilbert's Third Problem and the K Theory of Toric Varieties | |
1989 | Raoul Bott | Integral Homology of Real Flag Manifolds and Loop Spaces of Symmetric Spaces | |
1988 | Heisuke Hironaka | Newton Polyhedra without Coordinates | |
1988 | Robin Hartshorne | Cohomology of Normal bundles of curves in P and other Topics | |
1988 | Raoul Bott | Three Topics on Perturbation Analysis of Discrete Event Dynamic Systems | |
1988 | Sing-Tung Yau | Kaehler Metrics on Algebraic Manifolds | |
1988 | Limit Multiplications of Cusp Forms | ||
1988 | The Behavior of Stability under Equivariant Maps | ||
1988 | Yum-Tong Siu | Hyperbolic Surfaces | |
1988 | Ordered and unordered Periodic Points of Maps | ||
1987 | John Tate | Gamma Functions and Gauss Sums for Function Fields | |
1987 | Wilfried Schmid | Systems of Hodge Bundles and Uniformization | |
1987 | Benedict Gross | Lifting Endomorphisms of Formal Groups | |
1987 | Barry Mazur | Iwasawa theory at Multiplicative Primes | |
1987 | Benedict Gross | Heights and L-Series | |
1987 | Barry Mazur | Arithmetic of p-adic Modular Forms | |
1987 | Arthur Jaffe | Degree Theory of Wiener Maps and Supersymmetric Quantum Mechanics | |
1987 | Nancy Ann Lynch (MIT) | Topics in Distributed Algorithms | |
1987 | Benedict Gross and Barry Mazur | Supersingular Primes of a Given Elliptic Curve over a Number Field | |
1987 | Barry Mazur | Deformation theory of Galois Representations | |
1987 | Raoul Bott | Excursion in Cyclic Homology of Topological Algebras | |
1987 | Wilfried Schmid | Connections between Representations of Lie Groups and Sheaf Cohomology | |
1986 | David Mumford | Applications of Equivariant Morse Stratifications | |
1986 | Nondegeneracy of Infinitesimal Invariants Associated to Normal Functions | ||
1986 | John Tate | p-adic Periods as Moduli for Schottky Curves of Genus Two | |
1986 | Shlomo Sternberg | On Supergeometric Structures | |
1986 | Shannon Entropy and the Central Limit Theorem | ||
1986 | Philip Griffiths | On Local Torelli for Extremal Varieties | |
1986 | Stability and Canonical Metrics in Infinite Dimensions | ||
1986 | Local Heightson Families of Abelian Varieties | ||
1985 | Heisuke Hironaka | Sandwiched Singularities and the Nash Resolution for Surfaces | |
1985 | Bounds on Irregularity of Surfaces of General Type | ||
1985 | David Mumford | Prym Varieties and the Geodesic Flow on SO(n) | |
1985 | Heisuke Hironaka | Rank Conditions on Sub-Varieties of Grassmannians | |
1985 | David Mumford | Families of Rational Maps and Iterative Root-Finding Algorithms | |
1985 | David Kazhdan | On the Characters of the Representations of Division Algebras over a Weak Field | |
1985 | Barry Mazur | On the Canonical Closure of the Universal Elliptic Curve over Xl(n) | |
1985 | Raoul Bott | Functional Determinants and Applications to Geometry | |
1985 | Yum-Tong Siu | Positivity of the Curvature of the Weil-Petersson Metric on the Moduli Space of Stable Vector Bundles | |
1985 | On Higher Order Conservation Laws | ||
1985 | Wilfried Schmid | Special K-Types and the Beilinson-Bernstein Realization | |
1984 | Raoul Bott | Singularities in Moduli Spaces of Yang-Mills Fields | |
1984 | Characterization of Jacobian Varieties in Terms of Soliton Equations | ||
1984 | Barry Mazur | The Tate-Shafarevich Group of the Jacobian of a Quotient of the Fermat Curve | |
1984 | Wilfried Schmid | Discrete Characters on Non-Riemannian Symmetric Spaces | |
1984 | Barry Mazur | Analytic Multiplicity One Theorems for GL (n) | |
1984 | Wilfried Schmid | Hyperfunction Solutions of the Zero Rest Mass | |
1984 | Barry Mazur | On Zeta Functions Associated with the Space of Binary Cubic Forms with Coefficients in a Function Field | |
1984 | David Mumford | Compactification of Siegel Moduli Schemes | |
1984 | Gerald Sacks | B-Degrees for Weakly Inadmissible B | |
1983 | Involutive Hyperbolic Differential Systems | ||
1983 | Barry Mazur | Integral Points on Varieties | |
1983 | David Mumford | Construction of Holomorphic Differential Forms on the Moduli Space of Abelian Varieties | |
1983 | David Mumford | Hyperelliptic Curves and Solitons | |
1983 | David Kazhdan | Etale Cohomology and Arithmetic of Semisimple Groups | |
1983 | David Mumford | Topics in Algebraic Geometry | |
1983 | An Analogy of the Penrose Correspondence for Representations of U(p,q) on L2-Cohomology | ||
1983 | David Kazhdan | Theory of e-representations | |
1983 | Shlomo Sternberg | Integral Geometry on Compact Symmetric Spaces | |
1982 | Barry Mazur | Dirichlet Series Associated with the Space of Binary Cubic Forms with Coefficients in a Number Field | |
1982 | John Tate | The Neron-Tate Height On Elliptic Curves | |
1982 | George Mackey | Von Neumann Algebras Associated to Ergodic Actions of Countable Groups | |
1982 | John Tate | Algebraic Cycles on Abelian Varieties | |
1982 | Barry Mazur | On Certain Covers of the Universal Elliptic Curve | |
1982 | Raoul Bott | Homogeneous Connections and Yang-Mils Theory on Homogeneous Spaces | |
1982 | Raoul Bott | Hamiltonian Mechanics and Optimal Control | |
1982 | Phillip Griffiths | Special Fibers in Families of Plane Curves | |
1982 | Gerald Sacks | Independence Results Concerning Some Combinatorial Properties of the Continuum | |
1982 | The Gauss Map and Isometric Embedding | ||
1982 | Heisuke Hironaka | The Kahler Algebra and Analytic Equivalence of Isolated Hypersurfaces Singularities | |
1982 | Heisuke Hironaka | The Division Algorithm and the Hilbert Scheme | |
1981 | Barry Mazur | On Congruences Satisfied by Special Values of L-functions | |
1981 | Gerald Sacks | Aspects of E-Recursion | |
1981 | On the Arithmetic of CM Elliptic Curves in Zp-Extensions | ||
1981 | Barry Mazur | On J1(p) and the Arithmetic of the Kernel of the Eisenstein Ideal | |
1981 | Barry Mazur | On the Diophantine Arithmetic of Shimura Curves | |
1981 | Raoul Bott | Equivariant Morse Theory and Closed Geodesics | |
1981 | Gerald Sacks | Axiomatic Definitions of Programming Languages and Logics of Programs | |
1981 | Akihiro Kanamori | Iterated Perfect Set Forcing and Degrees of Constructibility | |
1981 | Phillip Griffiths | Hodge Theory | |
1981 | John Tate | Stark's Conjecture | |
1980 | Phillip Griffiths | Variation of Hodge Structure and the Local Torelli Problem | |
1980 | Phillip Griffiths | Semistable Degenerations of Enriques and Hyperelliptic Surfaces | |
1980 | Andrew Gleason | Stochastic Games: The Minmax Theorem | |
1980 | Shlomo Sternberg | Integral Geometry of Plane Complexes | |
1980 | The Kaehler algebra and analytic equivalence of isolated hypersurface singularities | ||
1979 | Gerald Sacks | Predicate-Oriented Database Search Algorithms | |
1979 | Andrew Gleason | Weakened Topologies for Lie Groups | |
1979 | Phillip Griffiths | Associated Curves and Plucker Formulas in Grassmannians | |
1978 | Shlomo Sternberg | Geometry of the Adjoint Representation of a Complex Semisimple Lie Algebra | |
1978 | Andrew Gleason | Zeros and Growth of Entire Functions of Order One and Maximal Type With an Application to the Random Signs Problem | |
1978 | David Mumford | Projective Stability of Ruled Surfaces | |
1978 | David Mumford | Quasi-Elliptic Surfaces in Characteristic Three | |
1978 | Phillip Griffiths | A Bound on the Geometric Genus of Projective Varieties | |
1978 | John Tate | Arithmetic on Elliptic Curves with Complex Multiplication | |
1978 | The Applications of Algebraic K-Theory to Intersection Theory | ||
1978 | Barry Mazur | Some Theorems on Azumaya Algebras | |
1978 | Essential Singularities of Entire Analytic Varieties | ||
1977 | Richard Brauer | Fusion in Nonabelian Groups of Order p3 | |
1977 | John Tate | Some Results on Classical Eisenstein Series and Modular Forms over Function Fields | |
1977 | John Tate | On the Local Langlands Conjecture for GL(2) | |
1977 | John Tate | Orbital Integrals on GL3 | |
1977 | The Hodge Theory of Flat Vector Bundles on a Complex Torus | ||
1977 | Barry Mazur | On p-adic Representations Arising From Descent on Abelian Varieties | |
1977 | Barry Mazur | P-adic Eisenstein Series for Function Fields | |
1977 | John Tate | A Comparison of the Automorphic Representations of GL (3) and its Twisted Forms | |
1977 | Phillip Griffiths | On the Geometry of Grassmannians | |
1977 | Lars Ahlfors | Deformations of Lie Groups and Lie Algebras | |
1977 | John Tate | Icosahedral Galois Representations | |
1977 | Raoul Bott | On the Smooth Cohomology of Groups of Diffeomorphisms | |
1976 | Raoul Bott | Refined Chern Classes for Foliations | |
1976 | Heisuke Hironaka | Deformations of L-cycles and the Chow Scheme | |
1976 | David Mumford | On Arithmetic Quotients of Bounded Symmetric Domains | |
1976 | George Mackey | Ergodic Actions of Product Groups | |
1976 | Garrett Birkhoff | Symmetry Groups of Partial Differential Equations | |
1976 | Shlomo Sternberg | Bernstein Polynomials and the Gauss-Manin Connection | |
1976 | Barry Mazur | Congruences Between Modular Forms and Implications for the Hecke Algebra | |
1976 | Heisuke Hironaka | Homology and Combinatorics of Ordered Sets | |
1975 | George Mackey | Ergodic Group Actions with Generalized Discrete Spectrum | |
1975 | Shlomo Sternberg | A Limit Theorem for Conditional Expectations with Applications to Probability Theory and Statistical Mechanics | |
1975 | Phillip Griffiths | Holomorphic Pseudogroup Structures on Quasiprojective Varieties | |
1975 | Andrew Gleason | Some Aspects of the Four Color Problem | |
1975 | Analytic Theory of Elliptic Curves with Split Multiplicative Reduction over Complete Rings | ||
1975 | David Mumford | On Degenerations of Algebraic Surfaces | |
1975 | Raoul Bott | Cohomology of Hamiltonian and Related Formal Vector Field Lie Algebras | |
1975 | David Mumford | Curvature on Algebraic Plane Curves | |
1975 | Raoul Bott | Continuous Cohomology of Spaces with Two Topologies | |
1975 | Barry Mazur | Diophantine and p-adic Analysis of Elliptic Curves and Modular Forms | |
1975 | George Mackey | Haar Measure and Convolution Algebras on Ergodic Groupoids | |
1975 | David Mumford | Cohomology of Flag Varieties on Characteristic p | |
1975 | Barry Mazur | Linking the Conjectures of Artin-Tate and Birch-Swinnerton-Dyer | |
1975 | Richard Brauer | On a Problem of E. Artin | |
1975 | David Mumford | Endomorphisms of Abelian Schemes | |
1975 | Lynn Loomis | Non-Linear Evolution Equations with Variable Norms | |
1975 | Andrew Gleason | Topics in Liftings and Stochastic Processes | |
1975 | Andrew Gleason | Small Rings in Critical Maps | |
1975 | Phillip Griffiths | Intrinsic Metrics and Measures on Compact Complex Manifolds | |
1975 | David Mumford | Polyhedral Reduction Theory in Self-Adjoint Homogeneous Cones | |
1975 | Phillip Griffiths | On the Theorem of Frenet | |
1974 | Lynn Loomis | Some Aspects of Balayage of Fourier Transforms | |
1974 | David Mumford | Deformations of Algebraic Varieties with Gm Action | |
1974 | David Mumford | P-adic Schottky Groups | |
1974 | John Tate | Two-descent for Elliptic Curves in Characteristic Two | |
1974 | Shlomo Sternberg | Ideals of Orbits of Nilpotent Lie Algebras | |
1974 | Raoul Bott | The Cohomology of Certain Algebraic Varieties | |
1974 | Richard Brauer | On a problem of E. Artin | |
1974 | Frederick Mosteller | Weak and Strong Averages in Probability and the Theory of Numbers | |
1974 | Saunders Mac Lane | On the Cohomology Theory of Fields | |
1974 | On the 2-primary Part of K2O and on Z2-extensions for Imaginary Quadratic Fields | ||
1974 | Stability of the Cut Locus | ||
1973 | George MacKey | Ergodic Affine Lebesgue G-Spaces | |
1973 | Andrew Gleason | Function Algebra Extensions and Analytic Structures | |
1973 | Some Aspects of Balayage of Fourier transforms | ||
1973 | Subalgebras of Division Algebras | ||
1973 | Galois Action on Division Points of Abelian Varieties with Many Real Multiplications | ||
1973 | |||
1973 | David Mumford | p-Adic Schottky Groups | |
1973 | Raoul Bott | Local Isomorphism of Riemannian Hermitian and Combinatorial Manifolds | |
1973 | |||
1973 | Transversality Properties of Topologically Stable Mappings | ||
1973 | Combinatorial Aspects of Lattice Theory with Applications for the Enumeration of Free Distributive Lattices | ||
1973 | Shlomo Sternberg | Topics on Universal Algebra | |
1973 | David Mumford | Valuative Criteria for Families of Vector Bundles on Algebraic Varieties | |
1973 | Barry Mazur | Universal Bounds on the Torsion and Isogenics of Elliptic Curves | |
1973 | Andrew Gleason | Interpolating Sequences in Polydisks | |
1973 | |||
1973 | |||
1973 | Andrew Gleason | Construction of Rings in Modular Lattices | |
1973 | George Mackey | On the Virtual Groups Defined by Ergodic Actions of R and Z | |
1973 | Convergence from an Algebraic Point of View | ||
1973 | |||
1973 | Iwasawa Invariants in Z1 extensions of Number Fields | ||
1972 | The Bracket Ring and Combinatorial Geometry | ||
1972 | George Mackey | Liftings in the Category of C* Algebras | |
1972 | Triangulation of 3-Manifolds: A Piecewise Linear Approach | ||
1972 | John Coates | Elliptic Curves of Prime Conductor | |
1972 | Shlomo Sternberg | Invariant Theory and the Cohomology of Infinite Lie Algebras | |
1972 | David Mumford | Non-singular Deformations of Space Curves using Determinantal Schemes | |
1972 | John Tate | Odd Perfect Numbers are Divisible by at least Seven Distinct Primes | |
1972 | Local Cohomology Dimension of Algebraic Varieties | ||
1972 | |||
1972 | Andrew Gleason | Direct Decompositions of Commutative Monoids | |
1972 | David Mumford | Towards Projectivity of the Space of Moduli of Stable Curves of a Given Genus | |
1972 | |||
1972 | David Mumford | A Study of Three-Dimensional Principally-Polarized Abelian Varieties | |
1972 | Raoul Bott | Curvature and the Eigenvalues of the Laplacian for Geometrical Elliptic Complexes | |
1972 | Triangulations of Two Manifolds with Local Properties | ||
1972 | Thom Polynomials for Contact Class Singularities | ||
1972 | David Mumford | Local Moduli of Abelian Varieties | |
1972 | Cauchy Problems with Random Initial Values in the Space of Tempered Distributions | ||
1971 | General-Valued Polarities | ||
1971 | David Mumford | Deformations of Branched Covers and Equisingularity | |
1971 | Ordered Structures and Partitions | ||
1971 | Lynn Loomis | Complex Involutory Banach Algebras | |
1971 | John Tate | The Non-vanishing of L(1) for Certain Elliptic Curves | |
1971 | Round-off Error in the Numerical Solution of Retarded Ordinary Differential Equations | ||
1971 | |||
1970 | Lars Ahlfors | Probabilistic Methods in Combinatorial Theory | |
1970 | Andrew Gleason | Properties of Isometrics and Almost Isometrics of Some Function Algebras | |
1970 | Partial Algebras | ||
1970 | Raoul Bott | Singularities of Maps and Characteristic Classes | |
1970 | Numerical Invariants and Gamma Products of Graphs | ||
1970 | David Mumford | Contributions to the Theory of Positive Embeddings in Algebraic Geometry | |
1970 | Lars Ahlfors | Special Moduli and Theta Relations | |
1970 | Andrew Gleason | Homologies and Elations of Finite Projective Planes | |
1970 | Raoul Bott | Orderings of Ultrafilters | |
1969 | Andrew Gleason | The Structure Space of a Choquet Simplex | |
1969 | David Mumford | Ordinary Singularities of Projective Varieties | |
1969 | Barry Mazur | On the Structure of Purely Inseparable Field Extensions | |
1969 | Andrew Gleason | Individuals in Zermelo-Fraenkel Set Theory | |
1969 | |||
1969 | Andrew Gleason | Functional Differential Equations with General Perturbation of Argument | |
1969 | Richard Brauer | Finite Linear Groups in Six Variables | |
1969 | Mathematical Models of Economic Growth | ||
1969 | Numerical Invariants and Multiple Planes | ||
1969 | |||
1969 | David Mumford | The Picard Scheme of a Quotient Problem | |
1969 | Raoul Bott | Cobordism | |
1969 | Raoul Bott | The Cohomology of the Complement of a Submanifold | |
1968 | John Tate | Abelian Varieties over Finite Fields | |
1968 | Compactness in Relational Structures | ||
1968 | Barry Mazur | Algebraic K of Vector Bundles | |
1968 | On the Flat Cohomology of Finite Group Schemes | ||
1968 | P-adic Theta Functions | ||
1968 | Shlomo Sternberg | Curvature and Metric | |
1968 | The Structure of a Banach Algebra Invariant for Measure Preserving Automorphisms | ||
1968 | Nonunitary Representations and Harmonic Analysis of Some Solvable Lie Groups | ||
1968 | Shlomo Sternberg | The Coholomogy Theory of Transitive Moduales over the Primitive Infinite Lie Algebras | |
1968 | George Mackey | Measures on Locally Compact Groups with Certain Transformation Properties | |
1968 | Semigroup Product Formulas and Addition of Unbounded Operators | ||
1968 | David Mumford | On the Structure of Locally Compact Groups | |
1968 | Commuting Elements in Free Algebras and Related T+E225opics in Ring Theory | ||
1967 | Complete Abelian Groups and Direct Sum Decompositions | ||
1967 | Richard Brauer | Finite Linear Groups in Seven Variables | |
1967 | Lars Ahlfors | The External Property of Certain Teichmüller Mappings | |
1967 | John Tate | On Automorphisms of Local Fields | |
1967 | Andrew Gleason | Approximation Theory on Compact Manifolds and Lie Groups with Applications to Harmonic Analysis | |
1967 | David Mumford | Abelian Varieties over a Perfect Field and Dieudonne` Modules | |
1967 | The Conjecture of Birch and Swinnerton-Dyer for Constant Abelian Varieties over Function Fields | ||
1967 | Homemorphisms of Sn x Sl | ||
1967 | Andrew Gleason | Radical Banach Algebras and Formal Power Series | |
1967 | Shlomo Sternberg | Overdetermined Systems of Analytic Partial Difference Equations | |
1967 | Cohomology Rings of Commutative Formal Groups | ||
1966 | Existence Theorems for Surfaces of Constant Mean Curvature and Perturbations of a Liquid Globule in Equilibrium | ||
1966 | Andrew Gleason | Powers of Maximal Ideals in Function Algebras | |
1966 | Lynn Loomis | Unbounded Normal Operators on Banach Spaces | |
1966 | Raoul Bott | Secondary Characteristic Classin K-Theory | |
1966 | David Mumford | On Hilbert Schemes | |
1966 | On the Minimum Computation Time of Functions | ||
1966 | Topological Methods in the Algebraic Theory of Vector Lattices | ||
1966 | Lars Ahlfors | Conformal Invariants for Condensers | |
1965 | The Convergence of Difference Approximations to Cauchy Problems in the Space of Tempered Distributions | ||
1965 | Quasi-ordinary Singularities of Embedded Surfaces | ||
1965 | Raoul Bott | Kunneth Formulas for Bordism Theories | |
1965 | Classification of Demushkin Groups | ||
1965 | Oscar Zariski | Toward a Numerical Theory of Ampleness | |
1965 | Lynn Loomis | Types of Completeness in Locally Convex Spaces | |
1965 | Lynn Loomis | Decomposition of Centrally Reducible and of Reducible Functionals | |
1965 | Andrew Gleason | Functions Resembling Quotients of Measures | |
1964 | Richard Brauer | Character Sums and Difference Sets | |
1964 | John Tate | Infinitesimal Deformations of Singularities | |
1964 | Raoul Bott | Formal Theory of Linear overdetermined Systems of Partial Differential Equations | |
1964 | Richard Brauer | Groups and Group Rings | |
1964 | John Tate | Curves over Discrete Valuation Rings | |
1964 | Richard Brauer | Characters and Systems of Subgroups | |
1964 | Lynn Loomis | Modules of Holomorphic Vector-Valued Functions | |
1964 | Richard Brauer | P-Solvable Linear Groups | |
1964 | Raoul Bott | Classification of certain Types of Spaces | |
1964 | Integral Equations Associated with Hankel Convolutions | ||
1964 | Rational Approximations to Generalized Hypergeometric Functions | ||
1964 | Convolution Transforms whose Inversion Functions have Complex Roots | ||
1963 | Raoul Bott | Categories in Homotopy Theory | |
1963 | Enumerating p-Groups | ||
1963 | Convex Functions and Dual Extremum Problems | ||
1963 | John Tate | Curves of Genus 3 over Characteristic 2 | |
1963 | Polynomial Bases for Compact Sets in the Plane | ||
1963 | Theory of Covering Spaces | ||
1963 | John Tate | One-parameter Formal Lie Groups over p-adic Integer Rings | |
1963 | Lynn Loomis | Almost Periodic Functionals in the Conjugate Space of a Banach Algebra | |
1963 | Lars Ahlfors | Elementary Moduli for Teichmüller Space | |
1963 | Andrew Gleason | Natural Functors in Topology and Generalizations | |
1963 | The Curves of Genus 3 Defined over Z/2Z | ||
1963 | Richard Brauer | On Finite Linear Groups whose Order contains a Prime Larger than the Degree | |
1963 | Applications of the Herbrand Theorem | ||
1963 | Raoul Bott | Spaces of Paths on a Symmetric Space | |
1963 | Richard Brauer | On the Subgroups of SL (3,q) | |
1962 | Richard Brauer | On Ree's Series of Simple Groups | |
1962 | Cohomology of Artinian Group Schemes over Local Fields | ||
1962 | The Shape of Level Loci of Green's Function and other Harmonic Functions | ||
1962 | Recursive Well Orderings and Transfinite Progressions | ||
1962 | Lynn Loomis | Existence and Applications of Dimension Functions in Lattices | |
1962 | Oscar Zariski | Existence of the Moduli Scheme for Curves of any Genus | |
1962 | Lars Ahlfors | An External Length Problem and the Bilinear Relation on Open Riemann Surfaces | |
1962 | Andrew Gleason | Combinatorial Problems of Elementary Abelian Groups | |
1962 | Lynn Loomis | Atomic Orthocomplemented Lattices | |
1962 | On the Global Existence of Solutions of Quasi-Linear Parabolic Equations | ||
1962 | Shlomo Sternberg | Theory of Finite G-Structures | |
1962 | Hierarchies in Recursive Function Theory | ||
1962 | On the Representations of C-Algebras | ||
1962 | Lars Ahlfors | Teichmüller Spaces of Groups of the Second Kind | |
1962 | The Asymptotic Behavior of Some Non-linear Autonomous Systems | ||
1961 | On Conformal Maps of Regions of Infinite Connectivity | ||
1961 | John Tate | Cohomology of Abelian Varieties over Function Fields | |
1961 | Lynn Loomis | The Radon-Nikodym Theorem in Dimension Lattices | |
1961 | On Differentials in Function Fields | ||
1961 | Raoul Bott | Applications of Intersection Theory to Boundary Value Problems | |
1961 | Raoul Bott | The Lower Central Series for Free Group Complexes | |
1961 | Some Results in the Cohomology Theory of Finite Groups | ||
1960 | Lars Ahlfors | A Classification of Noncompact Surfaces | |
1960 | John Moore | Extensions and Cohomology Theory of Locally Compact Groups | |
1960 | Minimal and Relatively Minimal Models for the Function Field of an Algebraic Surface | ||
1960 | George Mackey | Multipliers on Abelian Groups | |
1960 | Oscar Zariski | On the Theory of Birational Blowing-Up | |
1960 | A Characterization of Certain Banach Function Spaces | ||
1960 | Some Results on a Generalization of the Character Table of a Finite Group | ||
1960 | Truncated Policies in Dynamic Programming | ||
1960 | The Cohomology Ring of a Finite Group | ||
1960 | Oscar Zariski | On Enriques' surfaces | |
1959 | George Mackey | On General Measure Theory | |
1959 | Andrew Gleason | A Characterization of Congruence Groups in Geometries of the Euclidean Type | |
1959 | Richard Brauer | On the Irreducible Modulat Representations of Finite Classical Groups | |
1959 | Minimal Metric Spaces | ||
1959 | Lars Ahlfors | Automorphisms and Coverings of Riemann Surfaces Mappings | |
1959 | Richard Brauer | On the Characters of Finite Solvable Groups | |
1959 | Lars Ahlfors | Inversion and Representation Theory of the Weierstrass Transform | |
1958 | Richard Brauer | The Representation of Finite Groups in Algebraic Number Fields | |
1958 | Computable Functionals | ||
1958 | Andrew Gleason | Closed Subalgebras of a Commutative Algebra over the Real Numbers | |
1958 | Some aspects on Polynomial Approximation | ||
1958 | Mixed Cauchy Problems and C-Semigroups | ||
1958 | External Metrics for a Class of Varational Problems Related to Extended Length | ||
1958 | Richard Brauer | A Generalization of a Theorem of Blichfeldt | |
1958 | Andrew Gleason | Some Theories on Transformation Groups | |
1958 | Lynn Loomis | Derivations in Commutative Semi-Simple Banach Algebras | |
1958 | On the Homology of Local Rings | ||
1958 | Lars Ahlfors | The Bilinear Relation on Open Riemann Surfaces | |
1957 | Andrew Gleason | On Fibre Spaces and Fibre Bundles | |
1957 | Raoul Bott | Regular Curves on Riemann Manifolds | |
1957 | On Canonical Conformal Maps of Multiply Connected Regions | ||
1957 | Problems in the Distribution of the Prime Numbers | ||
1956 | On Generalized Tchebycheff Polynomials | ||
1956 | Andrew Gleason | A Global Formulation of the Lie Theory of Transformation Group | |
1956 | Generalized Lambert Transforms | ||
1956 | New Simple Lie Algebras | ||
1955 | The scattering of electromagnetic radiation by a cyclindrical shell of finite length | ||
1955 | Lars Ahlfors | Variability Regions for the Univalent Functions and their Derivatives | |
1955 | George Mackey | Locally M-Convex Algebras | |
1955 | Lars Ahlfors | Conformal Invariants and Prime Ends | |
1955 | On the generalization of the notion of H*-algebra: Complemented algebras | ||
1955 | Inversion of the Laplace and Stieltjes transforms utilizing difference operators | ||
1955 | Lars Ahlfors | Contributions to the Problem of Type | |
1955 | George Mackey | Some Inequalities Related to Holder Inequality and Some Contributions to Lattice Theory | |
1955 | Induced potentials | ||
1955 | Local uniformization of algebraic surfaces over modular ground fields | ||
1954 | Properties of a special set of entire functions and their respective partial sums | ||
1954 | Richard Brauer | On Finite Groups Related to Permutation Groups of Prime Degrees | |
1954 | Lars Ahlfors | External Problems on Riemann Surfaces | |
1954 | On approximation and interpolation by functions analytic in a given region and an application to orthonormal systems | ||
1954 | Geometric aspects of integration theory | ||
1953 | On distortion at the boundary of a conformal mapping | ||
1953 | Overconvergent Taylor Series and the zeros of related polynomials | ||
1953 | On some special order statistics from a multinomial distribution | ||
1953 | Axially symmetric stokes flows | ||
1953 | Lynn Loomis | Spectral Theory for a Class of Non-Linear Operators | |
1953 | The totality of curves of genus g | ||
1953 | L1-structure in Banach Spaces | ||
1952 | |||
1952 | A topological analysis of differential equations in the large | ||
1952 | Methods in the location of zeros of families of polynomials of unbounded degree in circles sectors and other regions | ||
1952 | The Fredholm Theory in Banach Spaces | ||
1952 | On the theorem of Bertini on the variable singular points of a linear system | ||
1952 | |||
1951 | On the harmonic analysis of certain groups and semi-groups of operators | ||
1951 | Lars Ahlfors | Harmonic Functions on Open Riemann Surfaces | |
1951 | On the Cohomology theory of associative algebras | ||
1951 | Some estimates for external distance | ||
1951 | |||
1951 | |||
1950 | Iterative methods for solving partial difference equations of elliptic type | ||
1950 | On the characterization of Reynolds operators on the normed algebra of all continuous real-valued functions defined on a compact Hausdorff space | ||
1950 | Lynn Loomis | On the Generalization of the Notion of H*-Algebra: Complex Algebra | |
1950 | Equivalence concepts on an algebraic curve | ||
1950 | Lars Ahlfors | Transformations in Reproducing | |
1950 | |||
1950 | |||
1949 | Lars Ahlfors | Properties of Conformal Invariants | |
1949 | Lars Ahlfors | Representations of Finite Groups | |
1949 | Hausdorff measure in abstract metric spaces | ||
1948 | Tensor fields associated with Lipschitz cochains | ||
1948 | The extensibility of local Lie groups of transformations and groups on surfaces | ||
1948 | Some problems in conformal mapping | ||
1948 | Joseph Walsh | On the Degree of Approximation to Harmonic Functions by Harmonic Polynomials | |
1948 | Lars Ahlfors | Diophantine Aspects of Poincare Theta Functions | |
1947 | Non-commutative integration and abstract differential equations | ||
1947 | Homology with operators and mapping theory | ||
1947 | The Moduli of univalence and of p-valence of functions analytic in the unit circle | ||
1947 | Some studies of functions of exponential type | ||
1947 | Axially symmetric harmonic functions | ||
1947 | The third iterate of the Laplace transform | ||
1946 | Multiplicative Riemann integration in normed rings | ||
1945 | On the solutions of ordinary linear homogeneous differential equations of the second order in the complex domain | ||
1945 | Topologies for spaces of transformations | ||
1936-1945 | MANY ENTRIES ARE MISSING | ||
1936 | Generalized derivatives and approximation by polynomials | ||
1936 | On the measure of the critical values of functions | ||
1936 | The linear homogeneous group modulo p | ||
1935 | Topics in the theory of critical points | ||
1935 | On interpolation and approximation to an analytic function by rational functions with preassigned poles | ||
1935 | Certain invariants of closed extremals | ||
1935 | Extensions of partially ordered sets | ||
1935 | The minimizing of a singular quadratic functional | ||
1935 | I. Interpolation in transforms of the roots of unity II. The Jacobi interpolation series on the lemniscate of convergence | ||
1934 | On a class of polynomials which minimize definite integrals | ||
1934 | On the planer points of an analytic surface | ||
1934 | The index form associated with an extremaloid | ||
1934 | A class of completely monotonic functions every positive power of which is also completely monotonic | ||
1934 | Topics in the theory of binary forms | ||
1933 | Parallelism and equidistance in Riemannian geometry | ||
1933 | Invariant methods in the infinitesimal geometry of surfaces | ||
1933 | The theory of tables of group characteristics | ||
1932 | The coloring of graphs | ||
1932 | On the derivations of Newtonian and logarithmic potentials near the acting masses | ||
1932 | On the degree of convergence and overconvergence of polynomials of best simultaneous approximation to several functions analytic in distinct regions | ||
1932 | On the double pendulum and similar dynamical systems | ||
1932 | Sufficient conditions in the problem of the calculus of variations in n-space in parametric form and under general end conditions | ||
1932 | Infinite systems if ordinary differential equations with applications to certain second order non-linear partial differential equations of hyperbolic type | ||
1932 | On rigid motions in four dimensions with applications to the Laguerre geometry of three dimensions | ||
1932 | The boundary values of analytic functions | ||
1931 | The Birkhoff fluid theory of electricity | ||
1931 | Invariant functions of conservative surface transformations | ||
1931 | The approximation of harmonic functions in three dimensions by harmonic polynomials | ||
1930 | On the theory of quadratic fields | ||
1930 | Contributions to the restricted problem of three bodies | ||
1930 | Existence of critical points of harmonic functions of three variables | ||
1930 | (a) Geodesics on a two-dimensional Riemannian manifold with periodic coefficients (b) Poincare's rotation number and Morse's type number | ||
1930 | (a) on the expansion of harmonic functions in terms of harmonic polynomials (b) On approximation to an arbitrary function of a complex variable by polynomials | ||
1930 | Some properties of genesubspaces of a Riemannian space | ||
1930 | The problem if the calculations in m-space with end points variable on two manifolds | ||
1930 | The cellular division and approximation of regular spreads | ||
1929 | On the differential geometry of surfaces in non-Euclidean space | ||
1929 | Singular points of second order systems of real differential equations | ||
1929 | The problem of n bodies | ||
1929 | Exterior motion in the restricted problem of three bodies | ||
1929 | Relations between the critical points of a real analytic function of n independent variables | ||
1929 | Fourier representations | ||
1928 | On the oscillation of harmonic functions | ||
1928 | On the location of the roots of the Jacobian of two binary forms and of the derivative of a rational function | ||
1927 | On the theory of linear differential equations of infinite order | ||
1926 | Ordinary linear homogeneous differential equations of order n and the related expansion problems | ||
1926 | Fundamental transformations of surfaces | ||
1926 | On rejection to infinity and exterior motion in the restricted Problem of Three Bodies | ||
1926 | The group characteristics of the general and special quaternary linear homogeneous groups | ||
1926 | Studies on the gyroscope | ||
1925 | Boundary value problems of the third order and the allied expansions | ||
1925 | Contributions to the theory of Riemann spaces | ||
1924 | Some mean-value theorems connected with Cote's Method of Mechanical Quadature | ||
1924 | Linear spaces and their fixed points. | ||
1923 | (a) on certain differential equations of the second order (b) on certain systems of differential equations containing a parameter | ||
1923 | On the theory of discrete varieties | ||
1923 | A method of series in elastic with applications (I) to circular plates of constant or variable thickness | ||
1922 | Expansion theorems for solution of a Fredholm homogeneous integral equation of the second kind with kernel of non-symmetric type | ||
1922 | (a) Developments associated with a boundary problem not linear in the parameter (b) the boundary problems and developments associated with a system of ordinary linear differential equations of the first order | ||
1922 | The equilong transformations of Euclidean space | ||
1922 | The general theory of the linear partial q-difference equation and of the linear partial difference equation of the intermediate type | ||
1921 | The determination of the coefficients in interpolation formulae and a study of the approximate solution of integral equations | ||
1920 | On the location of the roots of the Jacobian of two binary forms | ||
1920 | (a) Existence Theorems for the General Real Self-Adjoint Linear System of the Second Order (b) Oscillation Theorems for the Real Self-Adjoint Linear System of the Second Order | ||
1919 | The Geometry of a Non-Euclidean Line-Sphere Transformation | ||
1919 | On the Zeros of Solutions of Linear Differential Equations | ||
1919 | (a) On Linear equations with an Infinite Number of Variables (b) on Infinite Systems of Linear Integral Equations (c) Flexural Deflections and Statically Indeterminate Beams | ||
1917 | Certain types of geodesic motion on a surface of negative curvature | ||
1917 | Linear integro-differential equations with a boundary condition | ||
1917 | On rational approximations to an irrational complex number | ||
1917 | Curves invariant under point-transformations of special type | ||
1916 | Some problems connected with the linear connectivity of manifolds | ||
1916 | Systems of pencils of lines in ordinary space | ||
1916 | Some integral tests for the convergence and divergence of infinite series | ||
1916 | The hypergeometric difference equation | ||
1915 | Conformal transformation of curvilinear angles | ||
1915 | Problems in the theory of ordinary linear differential equations with auxiliary conditions at more than two points | ||
1915 | On the degree of convergence of Birkhoff's series | ||
1914 | The calculus of variations as the limit of a problem in minimizing an algebraic sum | ||
1914 | Su alcuni caratteri di una serie algebriea e la formola di de Jonquieres per serie qualsiasi | ||
1913 | On the functions of a complex variable defined by an ordinary differential equation of the first order and first degree | ||
1913 | An analytic treatment of the conic as an element of space of three dimensions | ||
1913 | Implicit functions defined by equations with vanishing Jacobian | ||
1913 | Oriented circles in space | ||
1912 | Problems connected with linear difference equations of the second order with special reference to equations with periodic coefficients | ||
1911 | Certain singularities of point-transformations in space of three-dimensions | ||
1910 | Vector functions of a point | ||
1910 | Volterra's integral equation of the second kind with discontinuous kernel | ||
1909 | On some problems in conformal mapping | ||
1909 | Certain singularities of transformations of two real variables | ||
1908 | On the theory of convergence factors and some of its applications | ||
1908 | The invariants of linear differential expressions | ||
1907 | A contribution to the theory of trigonometric and zonal harmonic series | ||
1906 | Brilliant points | ||
1905 | On the problem of analytic extension as applied to the functions defined by power series | ||
1904 | An arithmetic treatment of some problems in analysis situs | ||
1903 | Binary Families in a triply connected region with especial reference to hypergeometric families | ||
1902 | Regular singular points of a system of homogeneous linear differential equations of the first order | ||
1901 | On the invariants of quadratic differential forms | ||
1901 | The parametric representation of the neighborhood of a singular point of an analytic surface | ||
1898 | On linear differential equations of the third and fourth orders in whole solutions exist certain homogeneous relations | ||
1898 | The variation of latitude | ||
1897 | Systems of revolution and their relation to conical systems in the theory of Lame's products | ||
1897 | On the Roots of the hypergeometric and Bessel's Functions | ||
1895 | On the Properties of functions defined by the partial equation | ||
1889 | Bessel's Functions | ||
1887 | Surfaces having the principal radii of curvature at each point numberically equal but of opposite sign | ||
1886 | A contribution to the theory of the general equation of the sixth degree | ||
1879 | The investigation of the constants of the micrometirc apparatus of the Merz equatorial of the observatory of Harvard College together with the discussion of the observations of the satellites of Mars observed therewith | ||
1873 | The heat of the sun |
Dissertations and Placements 2010-Present
Emily Dautenhahn Thesis: Heat kernel estimates on glued spaces Advisor: Laurent Saloff-Coste First Position: Assistant Professor at Murray State University
Elena Hafner Thesis: Combinatorics of Vexillary Grothendieck Polynomials Advisor: Karola Meszaros First Position: NSF Postdoctoral Fellow,, at University of Washington
Sumun Iyer Thesis: Dynamics of non-locally compact topological groups Advisor: Slawomir Solecki First Position: NSF Postdoctoral Fellow at Carnegie Mellon University in Pittsburgh
Sebastian Junge Thesis: Applications of Transferring the Ramsey Property between Categories Advisor: Slawomir Solecki First Position: Lecturer at Texas State University
Nicki Magill Thesis: Infinite Staircases for Hirzebruch Surfaces Advisor: Tara Holm First Position: NSF Postdoctoral Fellow at UC Berkeley
Prairie Wentworth-Nice Thesis: Finite Groups, Polymatroids, and Error-Correcting Codes Advisor: Edward Swartz First Position: Postdoctoral Teaching Fellow at Johns Hopkins University
Fiona Young Thesis: Dissecting an Integer Polymatroid Advisor: Edward Swartz First Position: Pursuing her own start-up in the math education technology space
Kimoi Kemboi Thesis: Full exceptional collections of vector bundles on linear GIT quotients Advisor: Daniel Halpern-Leistner First Position: Postdoc at the Institution for Advanced Study and Princeton
Max Lipton Thesis: Dynamical Systems in Pure Mathematics Advisor: Steven Strogatz First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology
Elise McMahon Thesis: A simplicial set approach to computing the group homology of some orthogonal subgroups of the discrete group Advisor: Inna Zakharevich First Position: Senior Research Scientist at Two Six Technologies
Andrew Melchionna Thesis: Opinion Propagation and Sandpile Models Advisor: Lionel Levine First Position: Quantitative Researcher at Trexquant
Peter Uttenthal Thesis: Density of Selmer Ranks in Families of Even Galois Representations Advisor: Ravi Kumar Ramakrishna First Position: Visiting Assistant Professor at Cornell University
Liu Yun Thesis: Towers of Borel Fibrations and Generalized Quasi-Invariants Advisor: Yuri Berest First Position: Postdoc at Indiana University Bloomington
Romin Abdolahzadi Thesis: Anabelian model theory Advisor: Anil Nerode First Position: Quantitative Analyst, A.R.T. Advisors, LLC
Hannah Cairns Thesis: Abelian processes, and how they go to sleep Advisor: Lionel Levine First Position: Visiting Assistant Professor, Cornell University
Shiping Cao Thesis: Topics in scaling limits on some Sierpinski carpet type fractals Advisor: Robert Strichartz (Laurent Saloff-Coste in last semester) First Position: Postdoctoral Scholar, University of Washington
Andres Fernandes Herrero Thesis: On the boundedness of the moduli of logarithmic connections Advisor: Nicolas Templier First Position: Ritt Assistant Professor, Columbia University
Max Hallgren Thesis: Ricci Flow with a Lower Bound on Ricci Curvature Advisor: Xiaodong Cao First Position: NSF Postdoctoral Research Fellow, Rutgers University
Gautam Krishnan Thesis: Degenerate series representations for symplectic groups Advisor: Dan Barbasch First Position: Hill Assistant Professor, Rutgers University
Feng Liang Thesis: Mixing time and limit shapes of Abelian networks Advisor: Lionel Levine
David Mehrle Thesis: Commutative and Homological Algebra of Incomplete Tambara Functors Advisor: Inna Zakharevich First Position: Postdoctoral Scholar, University of Kentucky
Itamar Sales de Oliveira Thesis: A new approach to the Fourier extension problem for the paraboloid Advisor: Camil Muscalu First Position: Postdoctoral Researcher, Nantes Université
Brandon Shapiro Thesis: Shape Independent Category Theory Advisor: Inna Zakharevich First Position: Postdoctoral Fellow, Topos Institute
Ayah Almousa Thesis: Combinatorial characterizations of polarizations of powers of the graded maximal ideal Advisor: Irena Peeva First position: RTG Postdoctoral Fellow, University of Minnesota
Jose Bastidas Thesis: Species and hyperplane arrangements Advisor: Marcelo Aguiar First position: Postdoctoral Fellow, Université du Québec à Montréal
Zaoli Chen Thesis: Clustered Behaviors of Extreme Values Advisor: Gennady Samorodnitsky First Position: Postdoctoral Researcher, Department of and Statistics, University of Ottawa
Ivan Geffner Thesis: Implementing Mediators with Cheap Talk Advisor: Joe Halpern First Position: Postdoctoral Researcher, Technion – Israel Institute of Technology
Ryan McDermott Thesis: Phase Transitions and Near-Critical Phenomena in the Abelian Sandpile Model Advisor: Lionel Levine
Aleksandra Niepla Thesis: Iterated Fractional Integrals and Applications to Fourier Integrals with Rational Symbol Advisor: Camil Muscalu First Position: Visiting Assistant Professor, College of the Holy Cross
Dylan Peifer Thesis: Reinforcement Learning in Buchberger's Algorithm Advisor: Michael Stillman First Position: Quantitative Researcher, Susquehanna International Group
Rakvi Thesis: A Classification of Genus 0 Modular Curves with Rational Points Advisor: David Zywina First Position: Hans Rademacher Instructor, University of Pennsylvania
Ana Smaranda Sandu Thesis: Knowledge of counterfactuals Advisor: Anil Nerode First Position: Instructor in Science Laboratory, Computer Science Department, Wellesley College
Maru Sarazola Thesis: Constructing K-theory spectra from algebraic structures with a class of acyclic objects Advisor: Inna Zakharevich First Position: J.J. Sylvester Assistant Professor, Johns Hopkins University
Abigail Turner Thesis: L2 Minimal Algorithms Advisor: Steven Strogatz
Yuwen Wang Thesis: Long-jump random walks on finite groups Advisor: Laurent Saloff-Coste First Position: Postdoc, University of Innsbruck, Austria
Beihui Yuan Thesis: Applications of commutative algebra to spline theory and string theory Advisor: Michael Stillman First Position: Research Fellow, Swansea University
Elliot Cartee Thesis: Topics in Optimal Control and Game Theory Advisor: Alexander Vladimirsky First Position: L.E. Dickson Instructor, Department of , University of Chicago
Frederik de Keersmaeker Thesis: Displaceability in Symplectic Geometry Advisor: Tara Holm First Position: Consultant, Addestino Innovation Management
Lila Greco Thesis: Locally Markov Walks and Branching Processes Advisor: Lionel Levine First Position: Actuarial Assistant, Berkshire Hathaway Specialty Insurance
Benjamin Hoffman Thesis: Polytopes And Hamiltonian Geometry: Stacks, Toric Degenerations, And Partial Advisor: Reyer Sjamaar First Position: Teaching Associate, Department of , Cornell University
Daoji Huang Thesis: A Bruhat Atlas on the Wonderful Compactification of PS O(2 n )/ SO (2 n -1) and A Kazhdan-Lusztig Atlas on G/P Advisor: Allen Knutson First Position: Postdoctoral Associate, University of Minnesota
Pak-Hin Li Thesis: A Hopf Algebra from Preprojective Modules Advisor: Allen Knutson First position: Associate, Goldman Sachs
Anwesh Ray Thesis: Lifting Reducible Galois Representations Advisor: Ravi Ramakrishna First Position: Postdoctoral Fellowship, University of British Columbia
Avery St. Dizier Thesis: Combinatorics of Schubert Polynomials Advisor: Karola Meszaros First Position: Postdoctoral Fellowship, Department of , University of Illinois at Urbana-Champaign
Shihao Xiong Thesis: Forcing Axioms For Sigma-Closed Posets And Their Consequences Advisor: Justin Moore First Position: Algorithm Developer, Hudson River Trading
Swee Hong Chan Thesis: Nonhalting abelian networks Advisor: Lionel Levine First Position: Hedrick Adjunct Assistant Professor, UCLA
Joseph Gallagher Thesis: On conjectures related to character varieties of knots and Jones polynomials Advisor: Yuri Berest First Position: Data Scientist, Capital One
Jun Le Goh Thesis: Measuring the Relative Complexity of Mathematical Constructions and Theorems Advisor: Richard Shore First Position: Van Vleck Assistant Professor, University of Wisconsin-Madison
Qi Hou Thesis: Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces Advisor: Laurent Saloff-Coste First Position: Visiting Assistant Professor, Department of , Cornell University
Jingbo Liu Thesis: Heat kernel estimate of the Schrodinger operator in uniform domains Advisor: Laurent Saloff-Coste First Position: Data Scientist, Jet.com
Ian Pendleton Thesis: The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds Advisor: Tara Holm
Amin Saied Thesis: Stable representation theory of categories and applications to families of (bi)modules over symmetric groups Advisor: Martin Kassabov First Position: Data Scientist, Microsoft
Yujia Zhai Thesis: Study of bi-parameter flag paraproducts and bi-parameter stopping-time algorithms Advisor: Camil Muscalu First Position: Postdoctoral Associate, Université de Nantes
Tair Akhmejanov Thesis: Growth Diagrams from Polygons in the Affine Grassmannian Advisor: Allen Knutson First position: Arthur J. Krener Assistant Professor, University of California, Davis
James Barnes Thesis: The Theory of the Hyperarithmetic Degrees Advisor: Richard Shore First position: Visiting Lecturer, Wellesley College
Jeffrey Bergfalk Thesis: Dimensions of ordinals: set theory, homology theory, and the first omega alephs Advisor: Justin Moore Postdoctoral Associate, UNAM - National Autonomous University of Mexico
TaoRan Chen Thesis: The Inverse Deformation Problem Advisor: Ravi Ramakrishna
Sergio Da Silva Thesis: On the Gorensteinization of Schubert varieties via boundary divisors Advisor: Allen Knutson First position: Pacific Institute for the Mathematical Sciences (PIMS) postdoctoral fellowship, University of Manitoba
Eduard Einstein Thesis: Hierarchies for relatively hyperbolic compact special cube complexes Advisor: Jason Manning First position: Research Assistant Professor (Postdoc), University of Illinois, Chicago (UIC)
Balázs Elek Thesis: Toric surfaces with Kazhdan-Lusztig atlases Advisor: Allen Knutson First position: Postdoctoral Fellow, University of Toronto
Kelsey Houston-Edwards Thesis: Discrete Heat Kernel Estimates in Inner Uniform Domains Advisor: Laurent Saloff-Coste First position: Professor of Math and Science Communication, Olin College
My Huynh Thesis: The Gromov Width of Symplectic Cuts of Symplectic Manifolds. Advisor: Tara Holm First position: Applied Mathematician, Applied Research Associates Inc., Raleigh NC.
Hossein Lamei Ramandi Thesis: On the minimality of non-σ-scattered orders Advisor: Justin Moore First position: Postdoctoral Associate at UFT (University Toronto)
Christine McMeekin Thesis: A density of ramified primes Advisor: Ravi Ramakrishna First position: Researcher at Max Planck Institute
Aliaksandr Patotski Thesis: Derived characters of Lie representations and Chern-Simons forms Advisor: Yuri Berest First position: Data Scientist, Microsoft
Ahmad Rafiqi Thesis: On dilatations of surface automorphisms Advisor: John Hubbard First position: Postdoctoral Associate, Sao Palo, Brazil
Ying-Ying Tran Thesis: Computably enumerable boolean algebras Advisor: Anil Nerode First position: Quantitative Researcher
Drew Zemke Thesis: Surfaces in Three- and Four-Dimensional Topology Advisor: Jason Manning First position: Preceptor in , Harvard University
Heung Shan Theodore Hui Thesis: A Radical Characterization of Abelian Varieties Advisor: David Zywina First position: Quantitative Researcher, Eastmore Group
Daniel Miller Thesis: Counterexamples related to the Sato–Tate conjecture Advisor: Ravi Ramakrishna First position: Data Scientist, Microsoft
Lihai Qian Thesis: Rigidity on Einstein manifolds and shrinking Ricci solitons in high dimensions Advisor: Xiaodong Cao First position: Quantitative Associate, Wells Fargo
Valente Ramirez Garcia Luna Thesis: Quadratic vector fields on the complex plane: rigidity and analytic invariants Advisor: Yulij Ilyashenko First position: Lebesgue Post-doc Fellow, Institut de Recherche Mathématique de Rennes
Iian Smythe Thesis: Set theory in infinite-dimensional vector spaces Advisor: Justin Moore First position: Hill Assistant Professor at Rutgers, the State University of New Jersey
Zhexiu Tu Thesis: Topological representations of matroids and the cd-index Advisor: Edward Swartz First position: Visiting Professor - Centre College, Kentucky
Wai-kit Yeung Thesis: Representation homology and knot contact homology Advisor: Yuri Berest First position: Zorn postdoctoral fellow, Indiana University
Lucien Clavier Thesis: Non-affine horocycle orbit closures on strata of translation surfaces: new examples Advisor: John Smillie First position: Consultant in Capital Markets, Financial Risk at Deloitte Luxembourg
Voula Collins Thesis: Crystal branching for non-Levi subgroups and a puzzle formula for the equivariant cohomology of the cotangent bundle on projective space Advisor: Allen Knutson FIrst position: Postdoctoral Associate, University of Connecticut
Pok Wai Fong Thesis: Smoothness Properties of symbols, Calderón Commutators and Generalizations Advisor: Camil Muscalu First position: Quantitative researcher, Two Sigma
Tom Kern Thesis: Nonstandard models of the weak second order theory of one successor Advisor: Anil Nerode First position: Visiting Assistant Professor, Cornell University
Robert Kesler Thesis: Unbounded multilinear multipliers adapted to large subspaces and estimates for degenerate simplex operators Advisor: Camil Muscalu First position: Postdoctoral Associate, Georgia Institute of Technology
Yao Liu Thesis: Riesz Distributions Assiciated to Dunkl Operators Advisor: Yuri Berest First position: Visiting Assistant Professor, Cornell University
Scott Messick Thesis: Continuous atomata, compactness, and Young measures Advisor: Anil Nerode First position: Start-up
Aaron Palmer Thesis: Incompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity Advisor: Timothy J. Healey First position: Postdoctoral fellow, University of British Columbia
Kristen Pueschel Thesis: On Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups Advisor: Timothy Riley First position: Postdoctoral Associate, University of Arkansas
Chenxi Wu Thesis: Translation surfaces: saddle connections, triangles, and covering constructions. Advisor: John Smillie First position: Postdoctoral Associate, Max Planck Institute of
David Belanger Thesis: Sets, Models, And Proofs: Topics In The Theory Of Recursive Functions Advisor: Richard A. Shore First position: Research Fellow, National University of Singapore
Cristina Benea Thesis: Vector-Valued Extensions for Singular Bilinear Operators and Applications Advisor: Camil Muscalu First position: University of Nantes, France
Kai Fong Ernest Chong Thesis: Face Vectors and Hilbert Functions Advisor: Edward Swartz First position: Research Scientist, Agency for Science, Technology and Research, Singapore
Laura Escobar Vega Thesis: Brick Varieties and Toric Matrix Schubert Varieties Advisor: Allen Knutson First position: J. L. Doob Research Assistant Professor at UIUC
Joeun Jung Thesis: Iterated trilinear fourier integrals with arbitrary symbols Advisor: Camil Muscalu First position: Researcher, PARC (PDE and Functional Analysis Research Center) of Seoul National University
Yasemin Kara Thesis: The laplacian on hyperbolic Riemann surfaces and Maass forms Advisor: John H. Hubbard Part Time Instructor, Faculty of Engineering and Natural Sciences, Bahcesehir University
Chor Hang Lam Thesis: Homological Stability Of Diffeomorphism Groups Of 3-Manifolds Advisor: Allen Hatcher
Yash Lodha Thesis: Finiteness Properties And Piecewise Projective Homeomorphisms Advisor: Justin Moore and Timothy Riley First position: Postdoctoral fellow at Ecole Polytechnique Federale de Lausanne in Switzerland
Radoslav Zlatev Thesis: Examples of Implicitization of Hypersurfaces through Syzygies Advisor: Michael E. Stillman First position: Associate, Credit Strats, Goldman Sachs
Margarita Amchislavska Thesis: The geometry of generalized Lamplighter groups Advisor: Timothy Riley First position: Department of Defense
Hyungryul Baik Thesis: Laminations on the circle and hyperbolic geometry Advisor: John H. Hubbard First position: Postdoctoral Associate, Bonn University
Adam Bjorndahl Thesis: Language-based games Advisor: Anil Nerode and Joseph Halpern First position: Tenure Track Professor, Carnegie Mellon University Department of Philosophy
Youssef El Fassy Fihry Thesis: Graded Cherednik Algebra And Quasi-Invariant Differential Forms Advisor: Yuri Berest First position: Software Developer, Microsoft
Chikwong Fok Thesis: The Real K-theory of compact Lie groups Advisor: Reyer Sjamaar First position: Postdoctoral fellow in the National Center for Theoretical Sciences, Taiwan
Kathryn Lindsey Thesis: Families Of Dynamical Systems Associated To Translation Surfaces Advisor: John Smillie First position: Postdoctoral Associate, University of Chicago
Andrew Marshall Thesis: On configuration spaces of graphs Advisor: Allan Hatcher First position: Visiting Assistant Professor, Cornell University
Robyn Miller Thesis: Symbolic Dynamics Of Billiard Flow In Isosceles Triangles Advisor: John Smillie First position: Postdoctoral Researcher at Mind Research Network
Diana Ojeda Aristizabal Thesis: Ramsey theory and the geometry of Banach spaces Advisor: Justin Moore First position: Postdoctoral Fellow, University of Toronto
Hung Tran Thesis: Aspects of the Ricci flow Advisor: Xiaodong Cao First position: Visiting Assistant Professor, University of California at Irvine
Baris Ugurcan Thesis: LPLP-Estimates And Polyharmonic Boundary Value Problems On The Sierpinski Gasket And Gaussian Free Fields On High Dimensional Sierpinski Carpet Graphs Advisor: Robert S. Strichartz First position: Postdoctoral Fellowship, University of Western Ontario
Anna Bertiger Thesis: The Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space Advisor: Allen Knutson First position: University of Waterloo, Postdoctoral Fellow
Mariya Bessonov Thesis: Probabilistic Models for Population Dynamics Advisor: Richard Durrett First position: CUNY City Tech, Assistant Professor, Tenure Track
Igors Gorbovickis Thesis: Some Problems from Complex Dynamical Systems and Combinatorial Geometry Advisor: Yulij Ilyashenko First position: Postdoctoral Fellow, University of Toronto
Marisa Hughes Thesis: Quotients of Spheres by Linear Actions of Abelian Groups Advisor: Edward Swartz First position: Visiting Professor, Hamilton College
Kristine Jones Thesis: Generic Initial Ideals of Locally Cohen-Macaulay Space Curves Advisor: Michael E. Stillman First position: Software Developer, Microsoft
Shisen Luo Thesis: Hard Lefschetz Property of Hamiltonian GKM Manifolds Advisor: Tara Holm First position: Associate, Goldman Sachs
Peter Luthy Thesis: Bi-parameter Maximal Multilinear Operators Advisor: Camil Muscalu First position: Chauvenet Postdoctoral Lecturer at Washington University in St. Louis
Remus Radu Thesis: Topological models for hyperbolic and semi-parabolic complex Hénon maps Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University
Jenna Rajchgot Thesis: Compatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane Advisor: Allen Knutson First position: Research member at the Mathematical Sciences Research Institute (fall 2012); postdoc at the University of Michigan
Raluca Tanase Thesis: Hénon maps, discrete groups and continuity of Julia sets Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University
Ka Yue Wong Thesis: Dixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories Advisor: Dan M. Barbasch First position: Postdoctoral fellow at Hong Kong University of Science and Technology
Tianyi Zheng Thesis: Random walks on some classes of solvable groups Advisor: Laurent Saloff-Coste First position: Postdoctoral Associate, Stanford University
Juan Alonso Thesis: Graphs of Free Groups and their Measure Equivalence Advisor: Karen Vogtmann First position: Postdoc at Uruguay University
Jason Anema Thesis: Counting Spanning Trees on Fractal Graphs Advisor: Robert S. Strichartz First position: Visiting assistant professor of mathematics at Cornell University
Saúl Blanco Rodríguez Thesis: Shortest Path Poset of Bruhat Intervals and the Completecd-Index Advisor: Louis Billera First position: Visiting assistant professor of mathematics at DePaul University
Fatima Mahmood Thesis: Jacobi Structures and Differential Forms on Contact Quotients Advisor: Reyer Sjamaar First position: Visiting assistant professor at University of Rochester
Philipp Meerkamp Thesis: Singular Hopf Bifurcation Advisor: John M. Guckenheimer First position: Financial software engineer at Bloomberg LP
Milena Pabiniak Thesis: Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology Advisor: Tara Holm First position: Postdoctoral associate at the University of Toronto
Peter Samuelson Thesis: Kauffman Bracket Skein Modules and the Quantum Torus Advisor: Yuri Berest First position: Postdoctoral associate at the University of Toronto
Mihai Bailesteanu Thesis: The Heat Equation under the Ricci Flow Advisor: Xiaodong Cao First position: Visiting assistant professor at the University of Rochester
Owen Baker Thesis: The Jacobian Map on Outer Space Advisor: Karen Vogtmann First position: Postdoctoral fellow at McMaster University
Jennifer Biermann Thesis: Free Resolutions of Monomial Ideals Advisor: Irena Peeva First position: Postdoctoral fellow at Lakehead University
Mingzhong Cai Thesis: Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties Advisor: Richard A. Shore First position: Van Vleck visiting assistant professor at the University of Wisconsin at Madison
Ri-Xiang Chen Thesis: Hilbert Functions and Free Resolutions Advisor: Irena Peeva First position: Instructor at Shantou University in Guangdong, China
Denise Dawson Thesis: Complete Reducibility in Euclidean Twin Buildings Advisor: Kenneth S. Brown First position: Assistant professor of mathematics at Charleston Southern University
George Khachatryan Thesis: Derived Representation Schemes and Non-commutative Geometry Advisor: Yuri Berest First position: Reasoning Mind
Samuel Kolins Thesis: Face Vectors of Subdivision of Balls Advisor: Edward Swartz First position: Assistant professor at Lebanon Valley College
Victor Kostyuk Thesis: Outer Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups Advisor: Karen Vogtmann First position: Knowledge engineering at Reasoning Mind
Ho Hon Leung Thesis: K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory Advisor: Reyer Sjamaar First position: Assistant professor at the Canadian University of Dubai
Benjamin Lundell Thesis: Selmer Groups and Ranks of Hecke Rings Advisor: Ravi Ramakrishna First position: Acting assistant professor at the University of Washington
Eyvindur Ari Palsson Thesis: Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator Advisor: Camil Muscalu First position: Visiting assistant professor at the University of Rochester
Paul Shafer Thesis: On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Advisor: Richard A. Shore First position: Lecturer at Appalachian State University
Michelle Snider Thesis: Affine Patches on Positroid Varieties and Affine Pipe Dreams Advisor: Allen Knutson First position: Government consulting job in Maryland
Santi Tasena Thesis: Heat Kernel Analysis on Weighted Dirichlet Spaces Advisor: Laurent Saloff-Coste First position: Lecturer professor at Chiang Mai University, Thailand
Russ Thompson Thesis: Random Walks and Subgroup Geometry Advisor: Laurent Saloff-Coste First position: Postdoctoral fellow at the Mathematical Sciences Research Institute
Gwyneth Whieldon Thesis: Betti Numbers of Stanley-Reisner Ideals Advisor: Michael E. Stillman First position: Assistant professor of mathematics at Hood College
Andrew Cameron Thesis: Estimates for Solutions of Elliptic Partial Differential Equations with Explicit Constants and Aspects of the Finite Element Method for Second-Order Equations Advisor: Alfred H. Schatz First position: Adjunct instructor of mathematics at Tompkins Cortland Community College
Timothy Goldberg Thesis: Hamiltonian Actions in Integral Kähler and Generalized Complex Geometry Advisor: Reyer Sjamaar First position: Visiting assistant professor of mathematics at Lenoir-Rhyne University
Gregory Muller Thesis: The Projective Geometry of Differential Operators Advisor: Yuri Berest First position: Assistant professor at Louisiana State University
Matthew Noonan Thesis: Geometric Backlund transofrmation in homogeneous spaces Advisor: John H. Hubbard
Sergio Pulido Niño Thesis: Financial Markets with Short Sales Prohibition Advisor: Philip E. Protter First position: Postdoctoral associate in applied probability and finance at Carnegie Mellon University
How long is a PhD dissertation? [Data by field]
The final piece of the PhD journey is the PhD dissertation. It takes many years to accumulate enough original and new data to fill out a dissertation to the satisfaction of experts in your field. Interestingly, the PhD dissertation length and content vary significantly based on the field you are studying and the publishing conventions.
A PhD can be anywhere from 50 pages to over 450 pages long. This equates to between about 20,000 words to 100,000 words. Most PhD theses are between 60,000 and 80,000 words long excluding contents, citations and references.
A PhD thesis contains different sections including an introduction, methods, results and discussion, conclusions, further work, and references. Each one of these different sections will vary in length depending on the field of study and your particular topic.
Ultimately, a PhD dissertation should contain as many pages and words as it takes to communicate the results of your multi-year investigation.
It is very rewarding to see your thesis come together as you are writing day after day. When I was writing my PhD dissertation I wrote the sections separately and my heart filled with joy when I finally put them all together and compile them into a single PDF document.
Counting the pages should not be the way to determine a PhD dissertation’s value but it certainly helps when your thesis is starting to look substantial in thickness.
How many pages should a PhD dissertation be?
A PhD dissertation should contain as many pages and words as it takes to outline the current state of your field and provide adequate background information, present your results, and provide confidence in your conclusions. A PhD dissertation will also contain figures, graphs, schematics, and other large pictorial items that can easily inflate the page count.
Here is a boxplot summary of many different fields of study and the number of pages of a typical PhD dissertation in the field. It has been created by Marcus Beck from all of the dissertations at the University of Minnesota.
Typically, the mathematical sciences, economics, and biostatistics theses and dissertations tend to be shorter because they rely on mathematical formulas to provide proof of their results rather than diagrams and long explanations.
On the other end of the scale, English, communication studies, political science, history and anthropology are often the largest theses in terms of pages and word count because of the number of words it takes to provide proof and depth of their results.
At the end of the day, it is important that your thesis gets signed off by your review committee and other experts in the field. Your supervisor will be the main judge of whether or not your dissertation is capable of satisfying the requirements of a PhD in your field.
If you want to know more about how long a Masters’s thesis and PhD dissertation is you can check out my other articles:
- How Long is a Masters Thesis? [Your writing guide]
- How long is a Thesis or dissertation? [the data]
Can a PhD dissertation be too long?
A PhD thesis should contain enough evidence and discussion to report on the most significant findings of your PhD research.
A PhD dissertation should not contain everything that you have done during your PhD. It should only include the data and information required to convince your PhD examining body that wraps up and tells the full story of particular lines of investigation.
Including random results, thoughts, or superfluous explanation can result in a dissertation that is unfocused. I have heard of music PhD is being described as too verbose and physical sciences PhD dissertations as being unfocused.
Therefore, a PhD thesis can be too long if the information it contains does not form a full and cohesive story.
One of my colleagues during their PhD removed an entire chapter from the thesis after writing it as the supervisor said that it needed more experiments to be a full story. They did not want to spend the next six months gathering the data and simply removed the chapter altogether.
How short can PhD dissertation be?
The shortest PhD dissertations are typically found in mathematics.
George Bernard Danzig was an American mathematical scientist who made contributions to industrial engineering and many other mathematical-related fields. An interesting miscommunication led to 1 of the shortest PhD theses ever.
In 1939 his professor wrote two problems on the blackboard and Danzig thought they were homeless assignments. He stated that they were harder than usual but handed in solutions to the surprise of the professor.
They were, in fact, open mathematical problems in statistics.
His professor said to bind the solution to the two problems together and submit them as his thesis – the total thesis length = 14 pages.
Obviously, most PhD theses and dissertations will be so much longer than that!
My PhD dissertation was 256 pages long. It was full of schematics, diagrams, and tables to demonstrate and communicate my findings.
I would say that most people’s PhD thesis experience will be closer to mine than Prof George Bernard Danzig’s.
Why PhD dissertations are typically so long
PhD dissertations are often over 200 pages long.
One of the primary reasons they are so long is that it is a single document that summarises many years of hard work. Also, summarising the research field to date and making sure that all of your references and citations are included so you avoid plagiarism will bolster the word count of the thesis dramatically.
Here are all of the reasons PhD dissertations tend to be so long.
Many years of work
PhD theses or dissertations contain many years of research and analysis.
In many of my YouTube videos I recommend that a PhD student work towards their PhD thesis by doing at least three hours of focused work every work day.
This amount of work quickly adds up.
Of course, not every bit of work makes it into the PhD dissertation but a lot of it does. It can be difficult to work out what to include or leave out of your thesis.
As a PhD student, I perfected the art of turning one experiment into many different types of grafts and schematics to fully explore the limits of my data. The graphs can take up a lot of space in your PhD thesis and, therefore, bolster the page count significantly.
In depth literature review
One of the most substantial parts of a PhD dissertation is the literature review.
The literature review can take up a huge portion of the early part of your PhD dissertation depending on the amount of data and publications in your field.
Writing an in-depth literature review requires just as much meticulous data analysis and searching as the central part of your dissertation.
Figures and schematics
Some fields end up producing a lot of figures and schematics.
My thesis had many full-page figures of atomic force microscopy experiments with much more explanation on subsequent pages.
As they say, a picture paints a thousand words and a dissertation can really benefit from having many schematics to highlight the important aspects of your findings.
References and citations
The recommended PhD dissertation word count from an institution or university does not include citations, references, or other thesis parts such as summary of abbreviations, table of figures, et cetera.
However, these components of your dissertation can take up many pages and add to the overall thickness of your PhD dissertation.
University formatting rules
University formatting rules will also dictate how you many pages your words take up.
I often get roasted on my YouTube channel for having doublespaced lines and wide margins. Unfortunately, this layout was dictated by my university before printing.
PhD dissertations often end up going into long-term storage and therefore, need to adhere to archival and standardised formatting rules.
Deep in the depths of the University of Newcastle, there is a copy of my thesis on a shelf. The formatting and binding rules mean that my thesis looks like everyone else’s.
Universities will often have their own requirements for PhD dissertation cover colour, quality, and type of paper. Even the quality of the paper can change the thickness of the PhD dissertation significantly.
PhD by publication
It is becoming increasingly common to submit a number of peer-reviewed papers bound together with supplementary information in between instead of a PhD dissertation.
The benefits of this to the researcher and university are:
- More early career peer-reviewed journals for career advancement
- an easier review process – they have already been peer-reviewed
- an early focus on publishing means better research outcomes for the researcher, supervisor, and Department.
- No mad rush at the end to finish a thesis
- continually writing peer-reviewed papers throughout your PhD helps with timely analysis and communication of results
Even though this option has been available to PhD students for a number of years, I have only known a handful of students actually submit their PhD via publication.
Nonetheless, having this option will suit some research fields better than others and lead to a more productive PhD.
Wrapping up
This article has been through everything you need to know about the length of a PhD dissertation and the common lengths of PhD dissertations for various fields.
Ultimately, there is no predefined length of a PhD .
A PhD thesis is as long as it needs to be to convince your examiners that you have contributed significantly enough to an academic field to be awarded the title of Dr of philosophy.
Mathematical and analytical theses tend to be shorter and can be as short as 50 pages (with one of the shortest being only 14 pages long). At the other end of the spectrum, PhD students in anthropology and history tend to produce the longest dissertations.
Dr Andrew Stapleton has a Masters and PhD in Chemistry from the UK and Australia. He has many years of research experience and has worked as a Postdoctoral Fellow and Associate at a number of Universities. Although having secured funding for his own research, he left academia to help others with his YouTube channel all about the inner workings of academia and how to make it work for you.
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PhD Dissertations
In 1909 the department awarded its first PhD to Grace M. Bareis , whose dissertation was directed by Professor Harry W. Kuhn. The department began awarding PhD degrees on a regular basis around 1930, when a formal doctoral program was established as a result of the appointment of Tibor Radó as a professor at our department. To date, the department has awarded over 800 PhD degrees. An average of approximately 15 dissertations per year have been added in recent times. Find below a list of PhD theses completed in our program since 1952. (Additionally, search Ohio State at Math Genealogy , which also includes some theses from other OSU departments.)
2024 | Castillo, Nicholas | On Rational Approximations, Resurgence and Riemann-Hilbert Problems | Ovidiu Costin |
2024 | Christopherson, Adam | Weak-type Regularity of the Bergman Projection on Non-smooth Domains | Kenneth Koenig |
2024 | Clause, Nathaniel | New Invariants and Algorithms for Persistence over Posets | Facundo Mémoli |
2024 | Goldman, Katherine | Shephard Groups | Jingyin Huang |
2024 | Genlik, Deniz | Holomorphic Anomaly Equations For [C /Z ] | Hsian-Hua Tseng |
2024 | Gülen, Aziz Burak | Algebraic-Combinatorial Perspectives on Persistence: Functorial Constructions via Möbius Inversion and Galois Connections | Facundo Mémoli |
2024 | Lee, Jonghoo | Brauer Group of Split Toric Variety and Split Toric Scheme | Roy Joshua |
2024 | Lee, Ray | Reaction-Diffusion Equations in Spatial Ecology | King-Yeung Lam |
2024 | Newton, Scott | Representability For Monoid Extensions | Sanjeevi Krishnan |
2024 | Packer, Daniel | Symmetrical Machine Learning | Dustin Mixon |
2024 | Sehgal, Kriti | Dynamics of the Hénon–Heiles System and Generalizing the Sokhotski-Plemelj Formula | Ovidiu Costin |
2024 | Terek Couto, Ivo | The Geometry and Structure of Compact Rank-one ECS Manifolds | Andrzej Derdzinski |
2024 | Xing, Hao | Number Theoretical and Dynamical Properties of Euclidean Lattices and Their Sublattices | Nimish Shah |
2023 | Charparro Sumalave, Gustavo | Lafont, Jean-Francois | |
2023 | Chen, Chen | Anderson, David | |
2023 | Gomez Flores, Mario | Memoli, Facundo | |
2023 | Pan, Amanda | Nguyen, Hoi | |
2023 | Super, Shidhesh | Tseng, Hsian-Hua | |
2023 | Zhou, Ling | Memoli, Facundo | |
2023 | Carr, Matthew | Harper, John | |
2023 | Casey, Ian | Anderson, David | |
2023 | Chen, Quan | Penneys, David | |
2023 | Mishra, Bhawesh | Bergelson, Vitaly | |
2023 | Liu, Baian | Loper, Alan | |
2023 | Su, Wei Hung | Xiu, Dongbin | |
2023 | Wei, Zhining | Luo, Wenzhi | |
2023 | Werf Vander, Andrew | Kahle, Matthew [Paquette, Elliot] | |
2023 | Zhang, Danyu | Gogolyev, Andriy | |
2022 | Ababneh, Ayat | Kahle, Matthew | |
2022 | Ackelsberg, Ethan | Bergelson, Vitaly | |
2022 | Andrejek, Luke | Best, Janet | |
2022 | Call, Benjamin | Thompson, Daniel | |
2022 | Campolongo, Elizabeth | Taylor, Krystal | |
2022 | Chen, Yuhang | Tseng, Hsian-Hua | |
2022 | Dell, Zachary | Penneys, David | |
2022 | Duncan, Paul | Kahle, Matthew | |
2022 | Farhangi, Sohail | Bergelson, Vitaly | |
2022 | Huston, Peter | Penneys, David | |
2022 | Jeon, Minyoung | Anderson, David | |
2022 | Kim, Jimin | Kahle, Matthew | |
2022 | Leung, Wing Hong | Holowinsky, Roman | |
2022 | Martínez Figueroa, Francisco | Kahle, Matthew | |
2022 | Mejia Cordero, Julian | Holowinsky, Roman | |
2022 | Oh, Josiah | Lafont, Jean-Francois | |
2022 | Sun, Jiawei | Xing, Yulong | |
2022 | Tsang, Ling Hei | Katz, Eric | |
2022 | Vargas Bernal, Esteban | Tien, Joseph | |
2022 | Wang, Qingsong | Memoli, Facundo | |
2022 | Wang, Yuda | Koenig, Kenneth | |
2022 | Yan, Pan | Cogdell, James | |
2022 | Yang, Ruize | Xing, Yulong | |
2022 | Zhang, Yilong | Clemens, Herbert | |
2022 | Zhou, Zixu | Dongbin, Xiu | |
2021 | Bainbridge, Gabriel | Krishnan, Sanjeevi | |
2021 | Bello, Jason | Sivakoff, David | |
2021 | Best, Andrew | Bergelson, Vitaly | |
2021 | Bruno, Nick | Loper, Kenneth Alan | |
2021 | Chen, Zhen | Xiu, Dongbin | |
2021 | Clark, Duncan | Harper, John | |
2021 | Clum, Charles | Mixon, Dustin | |
2021 | Ferre Moragues, Andreu | Bergelson, Vitaly | |
2021 | Harper, Matthew | Kerler, Thomas | |
2021 | Hernandez Palomares, Roberto | Penneys, David | |
2021 | Lim, Sunhyuk | Memoli, Facundo | |
2021 | Patel, Dhir | Hiary, Ghaith | |
2021 | Schonsheck, Nikolas | Harper, John | |
2021 | Shah, Aniket | Anderson, David | |
2021 | Wan, Zhengchao | Memoli, Facundo | |
2021 | Wang, Tianyu | Thompson, Daniel | |
2021 | Xie, Yuancheng | Kodama, Yuji | |
2021 | Zelada Cifuentes, Jose Rigoberto Enrique | Bergelson, Vitaly | |
2021 | Zhang, Han | Shah, Nimish | |
2020 | Antoniou, Austin | Loper, Kenneth Alan | |
2020 | Beckwith, Alexander | Luo, Wenzhi | |
2020 | Castillo, Andrew | Koenig, Kenneth | |
2020 | DeBoer, Neil | Carlson, Timothy | |
2020 | Horst, Michael | Johnson, Niles | |
2020 | Kim, Woojin | Memoli, Facundo | |
2020 | Mernik, Luka | McNeal, Jeffery | |
2020 | Ohl, Trent | Miller, Christopher | |
2020 | Osborne, Matthew | Tien, Joseph | |
2020 | Singhal, Kritika | Memoli, Facundo | |
2020 | Wang, Jun | Tseng, Hsian-Hua | |
2020 | Zhang, Runlin | Shah, Nimish | |
2020 | Zhang, Yu | Harper, John | |
2019 | Aggarwal, Keshav | Holowinsky, Roman | |
2019 | Carnovale, Marc | Bergelson, Vitaly | |
2019 | Chowdhury, Samir | Memoli, Facundo | |
2019 | Guo, Sheng | Guan, Bo | |
2019 | Khalil, Osama | Shah, Nimish | |
2019 | Meehan, Sean | Nguyen, Hoi | |
2019 | Okutan, Osman | Memoli, Facundo | |
2019 | Ritchey, Katherine | Kahle, Matthew | |
2019 | Xiong, Jue | McNeal, Jeffery | |
2019 | Xu, Chao | Moscovici, Henri | |
2019 | Yang, Pengyu | Shah, Nimish | |
2019 | Ye, Rongqing | Cogdell, James | |
2018 | Belfanti, Edward Michael | Cogdell, James | |
2018 | Blomquist, Jacobson | Harper, John | |
2018 | Glogic, Irfan | Costin, Ovidiu | |
2018 | Jo, Yeongseong | Cogdell, James | |
2018 | Kennedy, Christopher | Lafont, Jean-Francois | |
2018 | Khan, Gabriel | Zheng, Fangyang | |
2018 | Lin, Yongxiao | Holowinsky, Roman | |
2018 | McGregor, Daniel | Loper, Kenneth Alan | |
2018 | Moore, Daniel | Cogdell, James | |
2018 | Nash, Evan | Kennedy, Gary | |
2018 | Newman, John Andrew | Kahle, Matthew | |
2018 | Nowland, Kevin | Holowinsky, Roman | |
2018 | Renardy, Marissa | Chou, Ching-Shan | |
2018 | Richter, Florian | Bergelson, Vitaly | |
2018 | Sathaye, Bakul | Lafont, Jean-Francois | |
2018 | Shin, Yeonjong | Xiu, Dongbin | |
2018 | Staten, Corey | Johnson, Niles | |
2018 | Wang, Yilong | Kerler, Thomas | |
2018 | Yang, Xige | Xue, Chuan | |
2018 | Yu, Han Baek | Sivakoff, David | |
2017 | Adali, Ali | Tanveer, Saleh | |
2017 | Borland, Alexander | Kerler, Thomas | |
2017 | Dinitz, Thomas | Best, Janet | |
2017 | Glasscock, Daniel | Bergelson, Vitaly | |
2017 | Kim, Tae Eun | Tanveer, Saleh | |
2017 | Liu, Shenhui | Luo, Wenzhi | |
2017 | Parsons, Kyle | Kahle, Matthew | |
2017 | Senay Aras, Betul | Chou, Ching-Shan | |
2017 | Steward, Michael | Loper, Kenneth Alan | |
2017 | Swang, Theodore | Best, Janet | |
2017 | Wang, Yanli | Chou, Ching-Shan | |
2017 | Xia, Bingyu | Anderson, David | |
2017 | You, Fenglong | Tseng, Hsian-Hua | |
2016 | Buenger, Carl | Shah, Nimish | |
2016 | Cervantes, José | Moscovici, Henri | |
2016 | Edholm, Luke | McNeal, Jeffery | |
2016 | Le, Giang | Davis, Michael | |
2016 | Malen, Greg | Kahle, Matthew | |
2016 | Moreira, Joel | Bergelson, Vitaly | |
2016 | Schmidt, Benjamin | Anderson, David | |
2016 | Sun, Weizhou | Chou, Ching-Shan | |
2016 | Wang, Shi | Lafont, Jean-Francois | |
2016 | Zhang, Qing | Cogdell, James | |
2016 | Zheng, Cheng | Shah, Nimish | |
2015 | Baker, Charles | Costin, Ovidiu | |
2015 | Gubkin, Steven | McNeal, Jeffery | |
2015 | Hsu, Ting-Hao | Keyfitz, Barbara | |
2015 | Huang, Jihui | Kodama, Yuji | |
2015 | Lam, Wing Chung | Luo, Wenzhi | |
2015 | Liu, Yang | Moscovici, Henri | |
2015 | Nasca, Angelo | Bergelson, Vitaly | |
2015 | Noble, Laine | Lou, Yuan | |
2015 | Qi, Zhi | Holowinsky, Roman | |
2015 | Robertson, Donald | Bergelson, Vitaly | |
2015 | Sui, Zhenan | Guan, Bo | |
2015 | Talamo, James | Gerlach, Ulrich | |
2015 | Wang, Xiaohui | Golubitsky, Martin | |
2015 | Xia, Xiaoyue | Costin, Ovidiu | |
2015 | Yang, Tao | Moscovici, Henri | |
2015 | Ying, Hao | Keyfitz, Barbara | |
2015 | Zhang, Qing | Luo, Wenzhi | |
2014 | Bosna, Bora | Carlson, Timothy | |
2014 | Christopherson, John | Bergelson, Vitaly | |
2014 | Edgren, Neal | McNeal, Jeffery | |
2014 | Fotis, Samuel | Luo, Wenzhi | |
2014 | Jia, Yuhan | Kodama, Yuji | |
2014 | Kim, Jung Eun | Best, Janet | |
2014 | Miller, Jason | Kennedy, Gary | |
2014 | Nicol, Andrew | Lafont, Jean-Francois | |
2014 | Olmez, Faith | Best, Janet | |
2014 | Ozcakir, Ozge | Tanveer, Saleh | |
2014 | Park, Hyejin | Costin, Ovidiu | |
2014 | Poole, Daniel | Pittel, Boris | |
2014 | Ravindran, Hari | Luo, Wenzhi | |
2014 | Wang, Kun | Lafont, Jean-Francois | |
2014 | Yang, Lei | Shah, Nimish | |
2014 | Ye, Zhilin | Holowinsky, Roman | |
2013 | Acan, Huseyin | Pittel, Boris | |
2013 | Alexander, Samuel | Carlson, Timothy | |
2013 | All, Timothy | Sinnott, Warren | |
2013 | Banerjee, Sayanti | Best, Janet | |
2013 | Chen, Weitao | Chou, Ching-Shan | |
2013 | Estill, Charles | Chmutov, Sergei | |
2013 | George, Jennifer | Kerler, Thomas | |
2013 | Gibbins, Aliska | Davis, Michael W. | |
2013 | Greene, Ryan | Davis, Michael W. | |
2013 | Joecken, Kyle | Lafont, Jean-Francois | |
2013 | Kowalick, Ryan | Lafont, Jean-Francois | |
2013 | Perkins, Rudolph | Goss, David | |
2013 | Peterson, Nicholas | Pittel, Boris | |
2013 | Rosenblatt, Heather | Tanveer, Saleh | |
2013 | Son, Younghwan | Bergelson, Vitaly | |
2013 | Sun, Wei | Guan, Bo | |
2013 | Teh, Wen Chean | Carlson, Timothy | |
2013 | Tychonievich, Michael | Chris Miller | |
2013 | Vutha, Amit | Golubitsky, Martin | |
2013 | Waller, Bradley | Sinnott, Warren | |
2013 | Wiser, Justin | Golubitsky, Martin | |
2013 | Yu, Xun | Clemens, Herbert | |
2012 | Averill, Isabel | Lou, Yuan | |
2012 | Chai, Jingsong | Cogdell, James | |
2012 | Du, Dong | Burghelea, Dan | |
2012 | Easwaran, Hiranmoy | Bergelson, Vitaly | |
2012 | Gard, Andrew | Fangyang Zheng | |
2012 | Kim, Raeyong | Lafont, Jean-Francois | |
2012 | Lynd, Justin | Solomon, Ron | |
2012 | Sequin, Matthew | Kerler, Thomas | |
2012 | Sivaraman, Vaidyanathan | Robertson, G. Neil | |
2012 | Ustian, Alex | Shah, Nimish | |
2011 | Adduci, James | Mityagin, Boris | |
2011 | Danisman, Yusuf | Cogdell, James | |
2011 | Hui, Wing San | Zheng, Fangyang | |
2011 | Ji, Haixia | Feinberg, Martin | |
2011 | McDougal, Robert | Terman, David | |
2011 | Munther, Daniel | Lou, Yuan | |
2011 | Polo, Fabrizio | Bergelson, Vitaly | |
2011 | Ravisankar, Sivaguru | McNeal, Jeffery | |
2011 | Ross, Christopher Jon | Pittel, Boris | |
2011 | Samara, Marko | March, Peter | |
2011 | Valle, Raciel | Leary, Ian | |
2011 | Whitaker, Erica | Cogdell, James | |
2011 | Xie, Zhizhang | Moscovici, Henri | |
2011 | Zhang, Huaijian | Baker, Gregory | |
2011 | Zhang, Lizhi | Costin, Ovidiu | |
2010 | Ahn, Sungwoo | Terman, David | |
2010 | File, Daniel Whitman | Cogdell, James | |
2010 | Huang, Min | Costin, Ovidiu | |
2010 | Im, Jeong Sook | Baker, Gregory | |
2010 | Joshi, Janhavi | McNeal, Jeffery | |
2010 | Kadyrov, Shirali | Shah, Nimish | |
2010 | Khare, Niraj | Seress, Akos | |
2010 | Kilanowski, Phillip | March, Peter | |
2010 | Kim, Kyung-Mi | Cogdell, James | |
2010 | Lee, Gangyong | Rizvi, S. Tariq | |
2010 | Lim, Changhoon | Guan, Bo | |
2010 | Liu, Yu-Han | Clemens, Herbert | |
2010 | Mance, William | Bergelson, Vitaly | |
2010 | Peng, Na | Edgar, Gerald A. | |
2010 | Su, Shu | Kao, Chiu-Yen | |
2010 | Wang, Jie | Clemens, Herbert | |
2010 | Wang, Ying | Kao, Chiu-Yen | |
2010 | Werner, Nicholas | Loper, Alan | |
2010 | Ye, Ji | Tanveer, Saleh | |
2010 | Zeki, Mustafa | Terman, David | |
2010 | Zeytuncu, Yunus Ergin | McNeal, Jeffery | |
2010 | Zhang, Yanyan | Golubitsky, Martin | |
2009 | Altomare, Christian | Robertson, G. Neil | |
2009 | Bezugly, Andriy | Lou, Yuan | |
2009 | Griesmer, John | Bergelson, Vitaly | |
2009 | Joshi, Badal | Best, Janet | |
2009 | Kurt, Oguz | Robertson, G. Neil | |
2009 | Kwa, Kiam Heong | Gerlach, Ulrich | |
2009 | Li, Lingfei | Zheng, Fangyang | |
2009 | Liu, Sheng-Chi | Luo, Wenzhi | |
2009 | Luo, Guo | Baker, Gregory | |
2009 | McSweeney, John | Pittel, Boris | |
2009 | Mehta, Nishali | Seress, Akos | |
2009 | Pikula, Rafal | Bergelson, Vitaly | |
2009 | Puliyambalath, Naushad | Seress, Akos | |
2009 | Qiu, Zhi | Costin, Ovidiu | |
2009 | Shi, Ronggang | Einsiedler, Manfred | |
2009 | Swartz, Eric | Seress, Akos | |
2009 | Wang, Xueying | Terman, David | |
2009 | Xie, Chao | Baker, Gregory | |
2009 | Young, Justin | Rallis, Stephen | |
2009 | Yu, Yang | Baker, Gregory | |
2009 | Zhao, Peng | Luo, Wenzhi | |
2008 | Arms, Scott | Sinnott, Warren | |
2008 | Ault, Shaun | Fiedorowicz, Z. | |
2008 | Balachandran, Niranjan | Robertson, G. Neil | |
2008 | Hur, Suhkjin | Glover, Henry H. | |
2008 | Kar, Aditi | Chatterji, Indira | |
2008 | Khoury, Michael | Cogdell, James | |
2008 | McClain, Christopher | Robertson, G. Neil | |
2008 | Nikolov, Martin | Flicker, Yuval | |
2008 | Niu, Liang | Seress, Akos | |
2008 | Schnell, Christian | Clemens, Herbert | |
2008 | Xiong, Wei | March, Peter | |
2008 | Xu, Songyun | Clemens, Herbert | |
2008 | Yang, Keyan | Seress, Akos | |
2008 | Yeum, Ji-A | Pittel, Boris | |
2007 | Hambrock, Richard | Lou, Yuan | |
2007 | Hammett, Adam | Pittel, Boris | |
2007 | Lennon, Craig | Pittel, Boris G. | |
2007 | Park, Choongseok | Terman, David | |
2007 | Pavlov, Ronald | Bergelson, Vitaly | |
2007 | Pu, Ming | March, Peter | |
2007 | Qi, Dongwen | Davis, Michael | |
2007 | Schoenecker, Kevin | Wyman, Bostwick F. | |
2007 | Stey, George | McNeal, Jeffery D. | |
2006 | Dimitrov, Youri | Edgar, Gerald A. | |
2006 | Fu, Yun | Baker, Gregory | |
2006 | Guler, Dincer | Zheng, Fangyang | |
2006 | Lee, Seung Youn | March, Peter | |
2006 | McKinley, Scott | March, Peter | |
2006 | Oman, Gregory | Loper, Alan | |
2006 | Pitale, Ameya | Rallis, Steven | |
2006 | Tsoi, Man | Sandstede, B. & Lou, Y | |
2006 | Wang, Hongyuan | Zheng, Fangyang | |
2006 | Xia, Honggang | Luo, Wenzhi | |
2005 | Chan, Ping-Shun | Flicker, Yuval | |
2005 | Ghazaryan, Anna | Sandstede, Bjorn | |
2005 | Guloglu, Ahmet | Luo, Wenzhi | |
2005 | Kane, Abdoul | Terman, David | |
2005 | Kaygun, Atabey | Moscovici, Henri | |
2005 | Kennel, Lauren | McNeal, Jeffery | |
2005 | Manukian, Vahagn | Sandstede, Bjorn | |
2005 | Micu, Eliade Mihai | Robertson, G. Neil | |
2005 | Salminen, Adam | Linckelman, Markus | |
2005 | Wolfe, Adam | Seress, Akos | |
2004 | Antal, Tamas | Moscovici, Henri | |
2004 | Argesanu, George | Wyman, Bostwick F. | |
2004 | Herbig, Anne-Katrin | McNeal, Jeffery D. | |
2004 | Iancu, Aniela Karina | Wyman, Bostwick F. | |
2004 | Liu, Xing | Tanveer, Saleh | |
2004 | Malyushitsky, Sergey | Harada, Koichiro | |
2004 | Otto, Michael | Krötz, Bernhard & Stanton, Robert | |
2004 | Roman, Cosmin | Rizvi, Syed M.Tariq | |
2004 | Wang, Jin | Baker, Gregory | |
2003 | Bell, Robert William, II | Charney, Ruth M. | |
2003 | Boros, Dan | Davis, Michael W. | |
2003 | Golubeva, Natalia | Baker, Gregory R. | |
2003 | Gorodnyk, Oleksandr | Bergelson, Vitaly | |
2003 | Han, Zhongxian | Wyman, Bostwick F. | |
2003 | Lladser, Manuel | Pemantle, Robin A. | |
2003 | Mendris, Robert | Nemethi, Andras | |
2003 | Wang, Chian-Jen | Rallis, Stephen | |
2003 | Yablonsky, Eugene | Dynin, Alexander | |
2003 | Zhou, Xiangqian | Robertson, G. Neil | |
2002 | Aydin, Nuh | Ray-Chaudhuri, Dijen K. | |
2002 | Barbacioru, Catalin | Sinnott, Warren M. | |
2002 | Conrad, Eric | Milne, Stephen C. | |
2002 | Craciun, Gheorghe | Feinberg, Martin Robert | |
2002 | Fiala, Nick | Seress, Akos | |
2002 | Hu, Xiaodong | Moscovici, Henri | |
2002 | Jalics, Jozsi Zoltan | Terman, David | |
2002 | McCoy, Ted | Edgar, Gerald A. | |
2002 | Sachelarie, Vlad | Wyman, Bostwick F. | |
2002 | Sherer, Scott | Scott, James | |
2002 | Slone, Rodney | Lee, R. | |
2001 | Beli, Constantin | Hsia, John S. | |
2001 | Breitenbucher, Jon | Milne, Stephen C. | |
2001 | Korchagina, Inna | Solomon, Ronald | |
2001 | Liu, Youjian | Fitz, Michael | |
2001 | Marchenko, Vadim | Terman, David | |
2001 | Pham, Lan | Baker, Gregory R. | |
2001 | Pohlman, Matthew | Baker, Gregory R. | |
2001 | Stacklin, Thomas | Pittel, Boris G. | |
2001 | Xie, Xuming | Tanveer, Saleh | |
2000 | Arenas-Carmona, Luis | Hsia, John S. | |
2000 | Barbu, Adrian | Ash, Avner D. | |
2000 | Butkevich, Sergey | Bergelson, Vitaly | |
2000 | Cashy, John | Glover, Henry H. | |
2000 | Gonciulea, Constantin | Davis, Michael W. | |
2000 | Gries, Daniel | Mislin, Guido | |
2000 | Iskhakov, Igor | Davis, Michael W. | |
2000 | Nabavi, Ali | Ray-Chaudhuri, Dijen K. | |
2000 | Pavlov, Savva | Rallis, Stephen | |
2000 | Qian, Jin | Ray-Chaudhuri, Dijen K. | |
2000 | Ralfs, Arthur | Terman, David | |
2000 | Ramsey, John | Oz, Hayrani A. | |
2000 | Xie, Xuming | Tanveer, Saleh | |
2000 | Zhang, Shaobo | Myung, In Jae | |
1999 | Blackford, Jason | Ray-Chaudhuri, Dijen K. | |
1999 | Bucicovschi, Bogdan | Burghelea, Dan | |
1999 | Genyuk, Julia | Edgar, Gerald A. | |
1999 | Gorokhovsky, Alexander | Moscovici, Henri | |
1999 | Bondareva Humphreys, Natalia | Baishanski, Bogdan M. | |
1999 | Liu, Kan | Ray-Chaudhuri, Dijen K. & Sehgal, Surinder K. | |
1999 | Mihalas, Stelian | Robertson, G. Neil | |
1999 | Möller, Torsten | Crawfis, Roger | |
1999 | Nigussie, Yared | Robertson, G. Neil | |
1999 | Ragozzine, Charles | Ferrar, Joseph C. | |
1999 | Roberts, Joel Philip | Silverberg, Alice | |
1999 | Siap, Irfan | Ray-Chaudhuri, Dijen K. | |
1999 | Snyder, Brian | Goss, David | |
1999 | Szilárd, Ágnes | Nemethi, Andras | |
1999 | Yang, Zifeng | Goss, David | |
1999 | Yeh, Jieh-Shan | Ray Chaudhduri, Dijen | |
1999 | YU, HOSEOG | Rubin, Karl C. | |
1999 | ZHANG, LINGHAI | Terman, David | |
1998 | Golds, Jeffrey | Edgar, Gerald A. | |
1998 | Hartenstein, Margaret | Solomon, Ronald | |
1998 | HLAVACEK, JAN | Baishanski, Bogdan M. | |
1998 | Jalics, Miklos | Baker, Gregory R. | |
1998 | LARICK, PAUL | Bergelson, Vitaly | |
1998 | Lu, Qin | Mislin, Guido | |
1998 | MAKAROV, MIHAIL | Kappeler, Thomas | |
1998 | Mohácsy, Hedvig | Ray-Chaudhuri, Dijen K. | |
1998 | Renedo, Marco | Bergelson, Vitaly | |
1998 | WAYAND, LEE | Davis, Michael W. | |
1998 | ZENKOV, DMITRY | BLOCH, ANTHONY M. | |
19971997 | BALTEANU, CORNEL | FIEDOROWICZ, ZBIGNIEW | |
1997 | CHEN, YU QING | Glover, Henry H. | |
1997 | GALUP, LUIS | Baishanski, Bogdan M. | |
1997 | HLAVACEK, AMY | HUNEKE, J. PHILIP | |
1997 | Hofmann, Glenn | Nagaraja, H.N. | |
1997 | JOHNSON, BRYAN | Baishanski, Bogdan M. | |
1997 | Kim, Yongdai | Baatoszynski, Robert | |
1997 | Koperski, Jeffrey | Batterman, Robert | |
1997 | LEININGER, VERNE | Milne, Stephen C. | |
1997 | MAJOR, EMERY | Burghelea, Dan | |
1997 | NANCE, ANTHONY | DOWLING, THOMAS A. | |
1997 | STADLER, JONATHAN | Milne, Stephen C. | |
1997 | VOMPE, DMITRY | Baker, Gregory | |
1997 | WEISHAAR, ROBERT | Pittel, Boris | |
1997 | YAO, LIHUA | March, Peter | |
1997 | Ye, Jian | Kodama, Yuji | |
1997 | ZINOVIEV, DMITRII | Flicker, Yuval | |
1996 | Altobelli, Joseph | Charney, R. | |
1996 | BABIKOV, MARK | Ferrar, Joseph C. | |
1996 | BAGDASAROV, SERGEY | Mityagin, Boris | |
1996 | Carlson, Charles | Forest, M. Gregory | |
1996 | Chan, Shing-Wai | Moscovici, Henri | |
1996 | Chan, Wai Kiu | Hsia, John | |
1996 | CHERN, SHIKAI | Moscovici, Henri | |
1996 | Das, Manabendra | Edgar, Gerald A. | |
1996 | Degenhardt, Sheldon | Milne, Stephen C. | |
1996 | HUNT, DONALD | CARROLL, FRANCIS W. | |
1996 | JEON, INTAE | March, Peter | |
1996 | Lam, Ching Hung | Harada, Koichiro | |
1996 | Lame, John | Sinnott, Warren | |
1996 | MAHARRY, JOHN | Robertson, G. Neil | |
1996 | Morje, Prabhav | Harada, Koichiro | |
1996 | MULLINS, EDMOND N., JR | Edgar, Gerald A. | |
1996 | POPESCU, CRISTIAN | Rubin, Karl C. | |
1996 | POUFINAS, THOMAS | Mityagin, Boris | |
1996 | ROSENBERG, STEVEN | Sinnott, Warren | |
1996 | SHALACK, JULIE | Ash, Avner D. | |
1996 | SZABO, TIBOR | Seress, Akos | |
1996 | Tsolomitis, Antonis | Davis, W. | |
1996 | Tungol, Ronald | Pittel, Boris G. | |
1996 | Wong, ChiKun | Charney, Ruth | |
1996 | XIAO, YIMIN | TALAGRAND, MICHEL | |
1996 | ZHOU, JIANPING | Wyman, Bostwick F. | |
1995 | Bhatnagar, Gaurav | Milne, Stephen C. | |
1995 | Dixit-Radiya, Vibha | Panda, Dhabaleswar K. | |
1995 | Gupta, Sandeep | Huang, C.H. | |
1995 | Joung, Haewon | Nevai, Paul | |
1995 | Kessar, Radha | Solomon, Ronald | |
1995 | Lee, Cary | Dougherty, Randall | |
1995 | Lee, Yoonweon | Burghelea, Dan | |
1995 | Marcsik, John | Burghelea, Dan | |
1995 | McCutcheon, Randall | Bergelson, Vitaly | |
1995 | Oh, Jangheon | Sinnott, Warren | |
1995 | Peery, Thaddeus | Ozbay, Hitay | |
1995 | Pinter, Ferenc | Nevai, Paul | |
1995 | Snell, Michael | Baishanski, B. | |
1995 | Varga, Jozsef | Mityagin, Boris | |
1995 | Wai, Hon-kit | Burghelea, Dan | |
1995 | Weisz, Iván | Seress, Akos | |
1995 | Wu, Kuo-Chi | Kodama, Y. | |
1995 | Xiang, Qing | Ray-Chaudhuri, D.K. | |
1995 | Xu, Mingzhi | Rubin, Karl | |
1995 | Zhang, Jianxiang | Baishanski, Bogdan | |
1994 | Ashokkumar, C. R. | Yedavalli, Rama K. | |
1994 | Dharmatilake, Jack | Robertson, G. Neil | |
1994 | Giust, Steven | Wyman, Bostwick F. | |
1994 | Gonzalez-Aviles, Cristian | Rubin, Karl C. | |
1994 | Jiang, Dihua | Rallis, Stephen | |
1994 | Li, Kuo-tung | Rosenblatt, Joseph | |
1994 | Manjrekar, Rajesh | Ash, Avner | |
1994 | McClure, Mark | Edgar, Gerald A. | |
1994 | Schwartz, Peter | Rosenblatt, Joseph | |
1994 | Shao, You Yu | Hsia, John | |
1994 | Wu, Xiaohong | Dowling, Thomas | |
1994 | Zantout, Rached | Zheng, Yuan F. | |
1993 | Anderson, Michael | Ferrar, J. | |
1993 | Beleznay, F. | Foreman, Matthew | |
1993 | Belhadj, Mohamed | Aldemir, Tunc | |
1993 | Daquila, Richard | Carroll, Francis W. | |
1993 | Elder, Gove | Madan, Manohar L. | |
1993 | Huang, Xiaoming | Bojanic, Ranko | |
1993 | Lee, Euiwoo | Terman, David | |
1993 | Leou, Ying-Tyug | Friedman, Harvey | |
1993 | Ouyang, Mingqing | Neumann, Walter | |
1993 | Sofer, Adriana S. | Ash, Avner | |
1993 | Szabó, Tamás | Divis, Zita | |
1993 | Tang, Shu-Leung | Gold, Robert | |
1993 | Yang, Tzu-Yi | Glover, Henry H. | |
1993 | Zha, Xiaoya | Dowling, Thomas | |
1993 | Zhu, Tianbao | Ray-Chaudhuri, D.K. | |
1992 | Ahmed, Shamim | Klein, Charles A. | |
1992 | Bishop, Gregory | Carlson, Timothy | |
1992 | Cao, Jianzhong | Forest, M.G. | |
1992 | Gethner, Ellen | Parson, L. Alayne | |
1992 | Haaland, Inger | Bergelson, Vitaly | |
1992 | Icaza Perez, Maria | Hsia, John S. | |
1992 | Kane, Stephen | Mityagin, Boris | |
1992 | Kim, Jeongjin | Ray-Chaudhuri, D.K. | |
1992 | Krandick, Werner | Collins, George E. | |
1992 | Lang, Cheng-Lien | Terman, David | |
1992 | Leclerc, Anthony | Moore, Ramon E. | |
1992 | Ling, Tianwen | Friedman, Harvey M. | |
1992 | Liu, Kecheng | Foreman, Matthew | |
1992 | Narayani, Lakshmi | Ray-Chaudhuri, D.K. | |
1992 | Raqab, Mohammad | Nagaraja, Haikady N. | |
1992 | Reyes, Noli | Baishanski, B. | |
1992 | Shaw, Hong-Min | Ray-Chaudhuri, D.K. | |
1992 | Sheu, Shin-pyng | Forest, M. Gregory | |
1992 | Spieler, Barry | Charney, Ruth M. | |
1992 | Zhao, Yue | Robertson, Neil | |
1991 | Banaszak, Grzegorz | Sinnott, Warren | |
1991 | Blanchard, John | Mityagin, Boris | |
1991 | Brozovic, Douglas | Solomon, Ronald | |
1991 | Craighead, Robert | Carroll, F. W. | |
1991 | Dale, Wilbur Nolan | Smith, Malcolm C. | |
1991 | Donahue, Michael | Mityagin, Boris | |
1991 | Johnson, Jeremy | Collins, George E. | |
1991 | Manoharan, Palanivel | Burghelea, Dan | |
1991 | Mariasoosai, William | Baishanski, Bogdan M. | |
1991 | Némethi, András | Moscovici, Henri | |
1991 | O'Ryan Lermanda, Manuel | Shapiro, Daniel | |
1991 | Prabaharan, Kanagarajah | Sucheston, L. | |
1991 | Reinhold-Larsson, Karin B. | Rosenblatt, Joseph | |
1991 | Voon, Shu-Nan | Glover, Henry | |
1991 | Wang, Qi | Forest, M.G. | |
1991 | Xiong, Chuyu | Overman, Edward | |
1991 | Yan, Zhongde | Edgar, Gerald | |
1990 | Chen, Lin | Yesha, Y. | |
1990 | Chilakamarri, Kiran Babu | Robertson, Neil | |
1990 | Druschel, Kimberly | Davis, M. | |
1990 | Forrest, Alan Hunter | Bergelson, Vitaly | |
1990 | Gajda, Wojciech | Davis, M.W. | |
1990 | Iwakata, Yasushi | Dowling, Thomas | |
1990 | Lari-Lavassani, Ali | Lu, Yung-Chen | |
1990 | Lee, Doobum | Burghelea, Dan | |
1990 | Lovri, Miroslav | Derdzinski, A. | |
1990 | Prieto-Cox, Juan | Hsia, John S. | |
1990 | Rodriguez Villegas, Fernando | Sinnott, Warren | |
1990 | Song, Yongjin | Fiedorowics, Zbigniew | |
1990 | Szabo, Laszlo | Sucheston, Louis | |
1990 | Tam, Laying | Baishanski, Louis | |
1990 | Xia, Yining | Glover, Henry H. | |
1990 | Yu, Jenn-Hwa | Edgar, Gerald | |
1989 | Andaloro, Paul | Ferrar, Joseph C. | |
1989 | Anghel, Nicolae | Moscovici, Henri | |
1989 | Bajnok, Bela | Bannai, Eiichi | |
1989 | Bunge, John | Nagaraja, H.N. | |
1989 | Chen, Hua | Burghelea, Dan | |
1989 | Kwok, Wing Man | Bannai, Eiichi | |
1989 | Munemasa, Akihiro | Bannai, Eiichi | |
1989 | Oporowski, Bogdan | Robertson, Neil | |
1989 | Peric, Goran | Moscovici, Henri | |
1989 | Schram, Erin | Ray-Chaudhuri, D.K. | |
1989 | Wierdl, Mate | Bergelson, Vitaly | |
1989 | Wu, Fangbing | Moscovici, Henri | |
1988 | Bannai, Etsuko | Hsia, John Sollion | |
1988 | Fiedler, Joseph | Huneke, John P. | |
1988 | Ghanaat, Patrick | Ruh, Ernst Alfred | |
1988 | Jha, Shing-Whu | Nevai, Paul | |
1988 | Kim, Jae Moon | Gold, Robert | |
1988 | Moussong, Gabor | Davis, Michael W. | |
1988 | Reeder, Mark Stephen | Avner, Dolnick Ash | |
1988 | Rzedowski Calderón, Martha | Madan, Manohar Lal | |
1988 | Villa-Salvador, Gabriel | Madan, Manohar Lal | |
1988 | Wimelaratna, Ramasinghege | Davis, William Jay | |
1987 | Ali, Sayel | Baishanski, B.M. | |
1987 | Han, Sang-Geun | Sinnott, Warren | |
1987 | Lang, Mong-lung | Bannai, Eiichi | |
1987 | Ray, Phillip | Ferrar, J.C. | |
1987 | Song, Sung Yell | Bannai, Eiichi | |
1987 | Vitray, Richard | Robertson, Neil | |
1986 | Batra, Sharat | Wigen, Philip E. | |
1986 | Bezdek, Andras | Glover, Henry | |
1986 | Char, Shobha | Burghelea, Dan | |
1986 | Lee, Jong-Eao | Carroll, Francis | |
1986 | Manickam, Nachimuthu | Bannai, Eiichi | |
1986 | Miklós, Dezsö | Ray-Chaudhuri, D.K. | |
1986 | Sali, Attila | Bannai, Eiichi | |
1986 | Weaver, Robert | Robertson, Neil | |
1985 | Bauldry, William | Nevai, Paul | |
1985 | Brackebusch, Ruth | Edgar, Gerald A. | |
1985 | Burdick, Bruce | Huneke, Philip | |
1985 | Butts, Eric | Davis, William | |
1985 | Childress, Nancy | Gold, Robert | |
1985 | Cho, Chong-Man | Johnson, William B. | |
1985 | Choi, Sul-Young | Bannai, Eiichi | |
1985 | Guan, Puhua | Ash, Avner | |
1985 | Huang, Tayuan | Bannai, Eiichi | |
1985 | Kim, Myung-Hwan | Hsia, John S. | |
1985 | Narang, Kamal | Harada, K. | |
1985 | Seress, Akos | Ray-Chaudhuri, D.K. | |
1985 | Singer, Phyllis | Allen, Harry P. | |
1985 | Song, Hi Ja | Davis, William J. | |
1984 | Brink, James | Gold, Robert | |
1984 | Chidume, Charles | Davis, William J. | |
1984 | Frangos, Nicholas | Sucheston, Louis | |
1984 | Grove, John W., (John Whitaker) | Davis, William | |
1984 | Hemmeter, Joseph | Bannai, Eiichi | |
1984 | Hong, Yiming | Bannai, Eiichi | |
1984 | Ku, Jong-Min | Ferrar, Joseph C. | |
1984 | Sheen, Rong-Chyu | Nevai, Paul | |
1984 | Wajima, Masayuki | Harada, Koichiro | |
1984 | Woldar, Andrew | Solomon, Ronald | |
1982 | Bonan, Stanford | Nevai, Paul | |
1982 | Carothers, Neal | Davis, William | |
1982 | Cheng, Fuhua | Baishanski, Bogdan | |
1982 | Costello, Patrick | Hsia, John S. | |
1982 | D'Mello, Joseph | Cronheim, Arno | |
1982 | Gross, Francis | Ksienski, Aharon A. | |
1982 | Johnson, Sandra | Glover, Henry H. | |
1982 | Kirschenbaum, Marc | Glover, Henry H. | |
1982 | Mahoney, Carolyn | Dowling, Thomas A. | |
1982 | Oprea, John | Burghelea, Dan | |
1982 | Shan, Chin-Chi | Baishanski, Bogdan | |
1982 | Shih, Ching-Hsien | Robertson, Neil | |
1981 | Benham, James | Hsia, John S. | |
1981 | Brickell, Ernest | Ray-Chaudhuri, D.K. | |
1981 | DeLaurentis, John | Edgar, Gerald | |
1981 | Flinn, Patrick | Davis, William | |
1981 | Moon, Aeryung | Bannai, Eiichi | |
1981 | Young, Elmer | Glover, Henry | |
1979 | Gearhart, Thomas | Levine, Norman | |
1979 | Huffman, William | Drobot, S. | |
1979 | Kahn, Jeffry | Ray-Chaudhuri, D.K. | |
1979 | Lichtin, Benjamin | Lu, Yung-Chen | |
1979 | Roth, Robert | Ray-Chaudhuri, D.K. | |
1979 | Valentini, Robert | Cronheim, Arno | |
1979 | Woltermann, Michael | Sehgal, Surinder K. | |
1978 | Anacker, Steven | Dowling, T.A. | |
1978 | Brewster, Stephen | Homer, William | |
1978 | Decker, Richard | Glover, Henry | |
1978 | Ford, David | Zassenhaus, Hans | |
1978 | Ko, Hai-Ping | Dowling, T.A. | |
1978 | Lichtin, Benjamin | Lu, Yung Chen | |
1978 | Lovett, Jane | Ferrar, Joseph | |
1978 | Wang, Shinmin | Dowling, T.A. | |
1978 | Yang, Liow-Jing | Woods, Alan C. | |
1977 | Barnes, Martha | Wilson, Richard | |
1977 | LeFever, John | Ray-Chaudhuri, D.K. | |
1977 | Liu, Chung-Der | Baishanski, Bogdan | |
1977 | Nemzer, Daniel | Ray-Chaudhuri, D.K. | |
1976 | Alspach, Dale | Johnson, William B. | |
1976 | Astbury, Kenneth | Sucheston, L. | |
1976 | Catlin, Paul Allen | Dowling, T.A. | |
1976 | Chakravati, Kamal | Dowling, T.A. | |
1976 | Chang, Kuang-I | Dowling, T.A. | |
1976 | Ching, Wai-Sin | Bostwick, F. Wyman | |
1976 | Denig, William | Dowling, T.A. | |
1976 | Gbur, Mary Flahive | Divis, Bohuslav | |
1976 | Markot, Robert | Bannai, Eiichi | |
1976 | Pal, Sat | Leitzel, James R.C. | |
1976 | Yoder, Jeffery | Mickle, Earl J. | |
1976 | Baker, Ronald | Dowling, T.A. | |
1975 | Burell, Benjamin | Zibler, Joseph A. | |
1975 | Chan, Agnes | Ray-Chaudhuri, D.K. | |
1975 | Dennis, John | Mickle, Earl J. | |
1975 | Donaldson, John | Zassenhaus, Hans | |
1975 | Dor, Leonard | Johnson, William B. | |
1975 | Earnest, Andrew | Hsia, John S. | |
1975 | Johnson, Robert | Drobot, Stefan | |
1975 | Madden, Daniel | Madan, Manohar L. | |
1975 | Ploeger, Bernard | Baishanski, Bogdan | |
1975 | Scrandis, Ann | Zassenhaus, Hans | |
1975 | Sze, Michael Ming Chih | Sucheston, L. | |
1975 | Trushin, David | Allen, Harry P. | |
1975 | Wang, Chin San | Robertson, Neil | |
1974 | Assa, Steven | Harada, Koichiro | |
1974 | Dunham, William | Huneke, Philip | |
1974 | Howell, Russell | Bojanic, Ranko | |
1974 | Kuntz, Amy | Sucheston, Louis | |
1974 | Mayer, David | Brown, Harold | |
1974 | O'Neill, Larkin | Huneke, Philip | |
1974 | Higgins, Rada | On The Asymptotic Behavior Of Certain Sequences | Bojanic, Ranko |
1973 | Bieberich, Richard | Baishanski, Bogdan | |
1973 | Coon, Lawrence | Riner, John W. | |
1973 | Hansen, Henry | Woods, Alan | |
1973 | Klippert, John | Eustice, Dan | |
1973 | Mertens, Robert | Ross, Arnold E. | |
1973 | McLean, Jeffery | Yaqub, Jill C.D.S. | |
1973 | Peterson, Roger | Hsia, John S. | |
1973 | Sommers, Dean | Crosswhite, F. Joe | |
1973 | Sprague, Alan | Ray-Chaudhuri, D.K. | |
1973 | Ulrey, Michael | Ahlswede, Rudolf | |
1973 | Vijayan, Kulakkatt | Ray-Chaudhuri, D.K. | |
1973 | Wang, Paul Tiing | Kerr, Douglas S. | |
1973 | Winkler, William | Sucheston, L. | |
1973 | Wong, Kwok Chi | Brown, Robert | |
1972 | Agashe, Pushpa | Levine, N. | |
1972 | Delany, Matthew | Zassenhaus, Hans | |
1972 | Ekong, Victor | Bojanic, R. | |
1972 | Hovis, Robert | Levine, N. | |
1972 | Jurick, Robert | Trimble, Harold C. | |
1972 | Lee, You-Hwa | Bojanic, R. | |
1972 | Merklen, Héctor | Zassenhaus, Hans | |
1972 | Molnar, Edward | Mislin, Guido | |
1972 | Pomaredo, Rolando | Janko, Z. | |
1972 | Raber, Neal | Cronheim, A. | |
1972 | Smith, Fredrick | Janko, Z. | |
1972 | Zahroon, Fike | Trimble, Harold | |
1971 | Datta, Biswa | Ray-Chaudhuri, D.K. | |
1971 | Nelson Engle, Jessie | Mickle, E. | |
1971 | Falk, Daniel | Zassenhaus, Hans | |
1971 | Heiberg, Charles | Baishanski, Bogdan | |
1971 | Milles, Stephen | Trimble, Harold | |
1971 | McClure, Clair | Trimble, Harold | |
1971 | Karamanoukian, Zaven | Woods, A.C. | |
1971 | Lundgren, J. Richard | Janko, Z. | |
1971 | Pujara, Lakhpat | Dean, David | |
1971 | Richard, Howard | Trimble, Harold | |
1971 | Rosenblum, Lawrence | Woods, Alan | |
1971 | Sehnert, James | Woods, Alan | |
1971 | St. Andre, Richard | Levine, N. | |
1971 | Terrell, Thomas | Kregnel, U. | |
1971 | Veith, Wilbur | Carroll, F.W. | |
1970 | Anderson, Osiefield | Trimble, Harold | |
1970 | Biddle, James | Cronheim, A. | |
1970 | Dudgeon, Charles | Whitney, D. Random | |
1970 | Gemma, James | Ahlswede, Rudolf | |
1970 | Hanigan, Francis | Uotila, Urho A. | |
1970 | Hill, David | Dean, David | |
1970 | Hogan, Guy | Cronheim, A. | |
1970 | Johnson, Charles | Zassenhaus, Hans | |
1970 | Klein, Albert | Levine, N. | |
1970 | Logan, J. David | Drobot, S. | |
1970 | McFarland, Robert | Zassenhaus, Hans | |
1970 | Sachdeva, Usha | Sucheston, Louis | |
1970 | Stager, William | Levine, Norman | |
1970 | Sonn, Jack | Zassenhaus, Hans | |
1970 | Yanosko, Kenneth | Janko, Z. | |
1969 | Fong, Humphrey Sek-Ching | Sucheston, L. | |
1969 | Haines, David | Levine, Norman | |
1969 | Hale, Douglas | Davis, William | |
1969 | Hern, Thomas | Shapiro, J.M. | |
1969 | Heuvers, Konrad | Drobot, Stefan | |
1969 | Hull, David | Shapiro, J.M. | |
1969 | Kimble, Kenneth | Drobpt, Stefan | |
1969 | Krier, Nicholas | Yaqub, J. | |
1969 | Kunes, Laurence | Shapiro, J.M. | |
1969 | Liang, Joseph Jen-Yin | Zassenhaus, Hans | |
1969 | Mathis, Robert | Saltzer, Charles | |
1969 | Meeks, Joseph | Mickle, E. | |
1969 | Scott, Frank | Levine, Norman | |
1969 | Wee, Leben Li | Levine, Norman | |
1969 | Wilson, R. M. | Ray-Chaudhuri, D.K. | |
1968 | Block, Henry | Shapiro, J.M. | |
1968 | Bonar, Daniel | Carroll, F.W. | |
1968 | Brown, John | Kapp, Wolfgang | |
1968 | Girard, Dennis | Baishanski, Bogdan | |
1968 | Keck, David | Reichelderfer, P.V. | |
1968 | Koehl, Frederick | Carroll, F.W. | |
1968 | Konvisser, Marc | Kappe, Wolfgang | |
1968 | Lu, Yu-Mei Yu | Trimble, Harold C. | |
1968 | Nachman, Louis | Levine, N. | |
1968 | Parker, Donald | Kappe, Wolfgang | |
1968 | Phillips, Paul | Trimble, Harold C. | |
1968 | Plybon, Benjamin | Drobot, Stefan | |
1968 | Pu, Huay-min Huoh | Helsel, R.G. | |
1968 | Queen, Clifford | Zassenhaus, Hans | |
1968 | Riggle, Timothy | Trimble, Harold C. | |
1968 | Shook, Thurston | Levine, N. | |
1968 | Sternbach, Leonard | Dean, David W. | |
1968 | Whitford, Leslie | Baishanski, Bogdan | |
1967 | Caufield, Patrick | Levine, N. | |
1967 | DeVore, Ronald | Bojanic, R. | |
1967 | Kimbleton, Stephen | Shapiro, J.M. | |
1967 | Klimko, Eugene | Sucheston, Louis | |
1967 | Klimko, Lawrence | Sucheston, Louis | |
1967 | Olson, John | Zassenhaus, Hans | |
1966 | Brown, Harold | Zassenhaus, Hans | |
1966 | Caid, Larry | Davis, William | |
1966 | Deever, David | Albian, Alexander | |
1966 | Holden, Lyman | Trimble, Harold C. | |
1966 | Hopkins, Mark | Mickle, E. | |
1966 | Nikolai, Paul | Saltzer, Charles | |
1966 | Steinlage, Ralph | Mickle, E. | |
1965 | Aggarwal, Satish | Bambah, R.P. | |
1965 | Breiter, Thomas | Levine, N. | |
1965 | Boonyasombut, Virool | Shapiro, J.M. | |
1965 | Dumir, V. C. | Bambah, R.P | |
1965 | Frazier, Thyrsa | Reichelderfer, Paul V. | |
1965 | Hans-Gill, R. J. | Bamba, R.P. | |
1965 | Nelson, Larry | Rado, T. | |
1965 | Randels, James | Rado, T. | |
1964 | Anderson, Charles | Kleinfeld, E. | |
1964 | Brabenec, Robert | Helse, R.G. | |
1964 | Brooks, James | Reichelderfer, Paul V. | |
1964 | Chaney, Robin | Reichelderfer, Paul V. | |
1964 | Houghton, Charles | Mickle, E. | |
1964 | Maxwell, John | Reichelderfer, Paul V. | |
1964 | Pu, Hwang Wen | Helsel, R.G. | |
1963 | Coppage, William | Whitney, D.R. | |
1963 | Laffer, Walter | Mann, Henry B. | |
1963 | Lin, Shen | Rado, T. | |
1963 | McWorter, William | Abian, Alexander | |
1963 | Norris, Donald | Reichelderfer, Paul V. | |
1963 | Outcalt, David | Whitney, D.R. | |
1963 | Schaefer, Donald | Mickle, E. | |
1963 | Staley, David | Levine, N. | |
1962 | Dixon, Robert | Tull, J.P. | |
1962 | Duemmel, James | Reichelderfer, Paul V. | |
1962 | Hardy, F. Lane | Kleinfeld, E. | |
1962 | Robison, Donald | Whitney, R. | |
1962 | Ryeburn, David | Reichelderfer, Paul V. | |
1961 | Johnsen, Eugene | Ryser, H.J. | |
1961 | Leetch, James | Helsel, R.G. | |
1961 | Martino, Joseph | Whitney, D.R. | |
1960 | Craft, George | Reichelderfer, Paul V. | |
1960 | Weiler, Fred | Reichelderfer, Paul V. | |
1960 | Willke, Thomas | Whitney, D.R. | |
1959 | Maneri, Carl | Kleinfeld, Erwin | |
1959 | McCulloh, Leon | Mann, Henry B. | |
1959 | Menon, Manavazhi | Mann, Henry B. | |
1959 | Nemitz, William | Mickle, Earl | |
1958 | Haber, Robert | Ryser, H.J. | |
1958 | Silverman, Robert | Whitney, D.R. | |
1958 | Thompson, Robert | Reichelderfer, Paul V. | |
1958 | Tinsley, Marion | Ryser, H.J. | |
1958 | Parker, Ernest | Hall, Marshall | |
1955 | Lin, Chio-Shih | Mann, Henry B. | |
1955 | Parrish, Herbert | Helsel, R.G. | |
1954 | Crowley, Thomas | Helsel, R.G. | |
1954 | Fadell, Albert | Rado, T. | |
1954 | Neugebauer, Christoph | Mickle, E. | |
1954 | Zemlin, Richard | Hall, Marshall | |
1953 | Butts, Hubert | Mann, Henry B. | |
1953 | Dean, Richard | Hall, Marshall | |
1953 | Edwards, Miles | Mickle, E. | |
1953 | Evans, John | Lazar, Nathan | |
1953 | Hoy, Walter | Mann, Henry | |
1953 | Moranda Paul | Mann, Henry | |
1953 | Sterbenz, Pat | Reichelderfer, Paul V. | |
1952 | Fadell, Edward | Reichelderfer, Paul V. | |
1952 | Levine, Norman | Absolutely Continuous Product Transformations Of The Plane | Helsel, R.G |
1952 | Martin, E. Wainwright | Hall, Marshall | |
1952 | Mendenhall, Robert | Helsel, R.G. | |
1952 | Myers, William | Reichelderfer, Paul. V | |
1952 | Tinnappel, Harold | Mickle, E. | |
1951 | Marsaglia, George | Stochastic Processes And Classes Of Random Variables | Mann, Henry |
1950 | Hoyoke, Thomas | An Embedding Problem For Transitive Permutation Groups | Hall, Marshall |
1949 | Whitney, Donald Ransom | A Comparison of the Power of Nonparametric Tests and Tests Based on the Normal Distribution Under Nonnormal Alternatives | Mann, Henry |
1949 | Colquitt, Landon A. | On Paths Of Minimum Flight Time | Bamforth, Frederic |
1947 | Adney, Joseph Elliott | Hall, Marshall | |
1947 | Miser, Hugh | Generalized Conformal Representations of Fréchet Surfaces | Rado, Tibor |
1947 | William, Scott | On Essentially Absolutely Continuous Transformations | Rado, Tibor |
1946 | Woods, Cecil | A Restricted Class of Convex Functions | Rado, Tibor |
1945 | Ayer, Miriam | On Convergence In Length | Rado, Tibor |
1943 | Huskey, Harry | Contributions to the Problem of Geocze | Rado, Tibor |
1942 | Goffman, Casper | On The Converses Of Certain Theorems On The Symmetric Structure Of Sets And Functions | Henry Blumberg |
1942 | Helsel, Robert | A Geometrical Application of Intregal Means | Rado, Tibor |
1942 | Krabill, David | Some Matrices Whose Elements Are Functions Of One Variable | Bamforth, Frederic |
1942 | Westhafer, Robert | Singular Solutions Of Ordinary Differential Equations Of The First Order | Bamforth, Frederic |
1941 | Mickle, Earl | Hamiltonian And Quasi-Hamiltonian Functions Associated With Double Integral Variation Problems | La Paz, Lincoln |
1941 | Ringenberg, Lawrence | On Functions Of Lawrence | Rado, Tibor |
1941 | Schart, William | Conditions For Solutions Of Certain Differential Equations Which Have Specified Properties | Bamforth, Frederic |
1941 | Young, Paul | On The Approximation of Functions By Integral Means | Rado, Tibor |
1940 | Cox, Jr., William | On Cummutative Normal Matrices And Unitary Equivalence Of Matrices | Kuhn, Harry |
1939 | Hammer, Preston | Projective Geometries Over A Pseudo-Field | Rado, Tibor |
1939 | Kato. Chosaburo | Configuration N Sub 3 | Rado, Tibor |
1939 | Reichelderfer, Paul | Some Properties Of Continuous Transformations In The Plane | Rado, Tibor |
1939 | Snyder, Walter | On Functions Of Squares | Rado, Tibor |
1939 | Tepletsky, Benjamin | Stability And Periodicity Of Solutions Of Mathieu's Equation | Bamforth, Frederic |
1938 | Rodabaugh, Louis | The Solution of a Certain Linear Partial Differential Equation of the First Order | Bamforth, Frederic |
1937 | Kohlmetz, Dorothy | Certain Problems Of A Special Character In Convex Functions | Rado, Tibor |
1936 | Bailey, Alson | An Approach To The Study Of Conic Sections, Based On A Group Of Projective Transformations | Rado, Tibor |
1936 | Gleyzal, Andre | On Transfinite Real Numbers, General Orders, Riemannian And Finsler Spaces | Blumberg, Henry |
1936 | Hanson, Eugene | A Theorem Of Denjoy, Young And Saks. Ii. The Tau Limit | Blumberg, Henry |
1936 | Hummel, Paul | Continued Fractions And Matrices | MacDuffee, Cyrus |
1936 | Southard, Thomas | On Certain Projective Geometries and Their Relation to Algebra | Rado, Tibor |
1935 | Jenkins, Emerson | The Composition Of Quadratic Forms | MacDuffee, Cyrus |
1935 | Lewis, Fred | Some Properties Of An Infinite Class Of Collineation Groups | Kuhn, Harry |
1935 | Rinehart, Robert | Some Properties Of The Discriminant Matrices Of A Linear Associative Algebra | MacDuffee, Cyrus |
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What is expected in a masters thesis of a mathematics student?
What is the level of work expected in the masters thesis of a student of maths?
I know some people's works are worthy of publications while some involve only studying some topic in detail from a book and submitting a summary (since this is akin to a couple of courses, a year worth of work, in that topic in terms of content covered, I would consider this,which I believe is called a literature review thesis , as an extreme opposite of independent research work thesis).
But what is the "average" level of a MS thesis of a mathematics student? Is it usually closer to a literature review thesis or a research work thesis?
In particular, I would also like to know:
How much is it valued (if at all) when one applies for PhD? I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to absence of GRE like criterion there. Is this true?
Edit : After the wonderful existing answer explaining the case in Germany, I would really like to know the situation in US too. I expect a drastic difference due to the presence of GRE system but would like to know how much importance the thesis has, there.
PS: Please excuse me if one can find answers to some of these questions in already existing questions. I have searched, but couldn't find them. Please provide the links in those cases.
Also, anecdotal details will also be greatly appreciated. Thanks!
- graduate-admissions
- mathematics
- @user54981 Of course that would most certainly be there. – Neeraj Kumar Commented Jun 6, 2016 at 6:01
- 2 The difference between US/Canada and Europe is mainly due to the fact that in most European institutions, applicants to a PhD program are expected to held a Masters or equivalent degree, and the PhD program is often research only with close to no coursework. Compare to North American institutions where applicants to a PhD program are not expected to hold a Masters, and generally only hold a Bachelors degree, and where the program tends to be longer with a more significant coursework portion. – Willie Wong Commented Jun 8, 2016 at 13:40
- Note also that the European application process for entering a PhD program is often quite different from the typical North American one. (Search on this site if you want to know more; I'm sure it has been asked before.) – Willie Wong Commented Jun 8, 2016 at 13:41
- @NeerajKumar Not necessarily equations. Almost certainly inequalities such as the element relation. – Jacob Murray Wakem Commented Jun 8, 2016 at 15:35
- @JacobWakem I don't understand what the term element relation is but isn't the presence of inequalities dependent on the topic? For example, a thesis in algebraic topology or geometry is most likely to not use any inequalities but one in functional analysis or number theory may have a lot of it.. – Neeraj Kumar Commented Jun 9, 2016 at 4:03
3 Answers 3
I think this varies a lot. But for Germany your first question can be answers succinctly: In a Master's thesis you should show that you have potential for research .
On the other hand, expectations vary a lot between advisors. But certainly you do not have to prove a new theorem or develop a new theory.
How much is it valued (if at all) when one applies for PhD?
I can only answer for the situation where you apply in Germany. The thesis can be a door opener if it is topic closely related to the field where you want to do a PhD. Also a good mark is important. But also in Germany hiring professors will often contact your advisors or request a reference letter and this is much more important.
I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to no GRE like criterion. Is this true?
Not sure on this point since I can't provide a comparison with the US and also I am not sure if the situation is uniform with the EU.
- Thanks for the answer. As I mentioned, there are the two extremes in the kinds of thesis. In the first I can imagine the potential for research to be clearly visible( since they are doing actual research work) but how about the second case? If the work is only the study of a topic then? I doubt if it would reflect much on the potential to do research. Though one consideration that I can imagine is if the person spends his thesis studying on a certain topic then would it be of any advantage if person applies into that topic for PhD. Are such considerations taken into account? – Neeraj Kumar Commented May 26, 2016 at 15:37
- Sorry if this is not getting more concrete, but, e. g., a literature review thesis can or can not show research potential. If your question is: What do I have to do in a Master's thesis do get a PhD position, the answer is "Nobody can tell you in advance." Go ahead and choose a thesis topic you find thrilling and write a good thesis. – Dirk Commented May 26, 2016 at 16:27
From my knowledge of the US system (I did my graduate work in the US, and am currently a professor in the US), the average level of a masters thesis is relatively low. (That said, it usually does involve at least some original research).
The reason for this is the structure of Ph.D. programs in the US. Usually students are admitted to Ph.D. programs directly as undergraduates, and the first two years of the Ph.D. are similar to an MS program in Europe. Students who complete a Ph.D. don't generally write a masters thesis along the way. Rather, masters theses are usually written by students who decide in their second year not to continue with our Ph.D. program, but would still like to earn some sort of degree for their efforts. These theses are often weak (but sometimes are quite good).
Some students do use an MS as a stepping stone to Ph.D. programs elsewhere; indeed, I personally know students who successfully transferred to much stronger programs. Their MS-level work was much better than average.
In short: The degree itself won't be highly valued in the US, but doing an MS can lead to strong letters from your professors and research advisors, and these will be highly valued.
- Another complication with master's theses, in the U.S., is a perception that the student "will do a PhD thesis anyway" if they go on to a PhD program, and so there is less need for the master's thesis to include challenging research. The motivation for writing a master's thesis becomes different from the motivation for writing a PhD thesis. – Oswald Veblen Commented Jun 9, 2016 at 21:19
A great resource I have used to understand the quality of final thesis work for my primary focus is the Open Access Theses and Dissertations which has thousands of master's and Ph. D. final publications. Research this website using your topic and you will see what amount of research is involved, differences and similarities between schools, methodologies, etc.
In addition, a great site for further publications is http://Arxiv.org . Many thesis in the U.S. are 'sandwich' publications, involving an assortment of publications published while student is performing research.
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How To Write A Dissertation Or Thesis
8 straightforward steps to craft an a-grade dissertation.
By: Derek Jansen (MBA) Expert Reviewed By: Dr Eunice Rautenbach | June 2020
Writing a dissertation or thesis is not a simple task. It takes time, energy and a lot of will power to get you across the finish line. It’s not easy – but it doesn’t necessarily need to be a painful process. If you understand the big-picture process of how to write a dissertation or thesis, your research journey will be a lot smoother.
In this post, I’m going to outline the big-picture process of how to write a high-quality dissertation or thesis, without losing your mind along the way. If you’re just starting your research, this post is perfect for you. Alternatively, if you’ve already submitted your proposal, this article which covers how to structure a dissertation might be more helpful.
How To Write A Dissertation: 8 Steps
- Clearly understand what a dissertation (or thesis) is
- Find a unique and valuable research topic
- Craft a convincing research proposal
- Write up a strong introduction chapter
- Review the existing literature and compile a literature review
- Design a rigorous research strategy and undertake your own research
- Present the findings of your research
- Draw a conclusion and discuss the implications
Step 1: Understand exactly what a dissertation is
This probably sounds like a no-brainer, but all too often, students come to us for help with their research and the underlying issue is that they don’t fully understand what a dissertation (or thesis) actually is.
So, what is a dissertation?
At its simplest, a dissertation or thesis is a formal piece of research , reflecting the standard research process . But what is the standard research process, you ask? The research process involves 4 key steps:
- Ask a very specific, well-articulated question (s) (your research topic)
- See what other researchers have said about it (if they’ve already answered it)
- If they haven’t answered it adequately, undertake your own data collection and analysis in a scientifically rigorous fashion
- Answer your original question(s), based on your analysis findings
In short, the research process is simply about asking and answering questions in a systematic fashion . This probably sounds pretty obvious, but people often think they’ve done “research”, when in fact what they have done is:
- Started with a vague, poorly articulated question
- Not taken the time to see what research has already been done regarding the question
- Collected data and opinions that support their gut and undertaken a flimsy analysis
- Drawn a shaky conclusion, based on that analysis
If you want to see the perfect example of this in action, look out for the next Facebook post where someone claims they’ve done “research”… All too often, people consider reading a few blog posts to constitute research. Its no surprise then that what they end up with is an opinion piece, not research. Okay, okay – I’ll climb off my soapbox now.
The key takeaway here is that a dissertation (or thesis) is a formal piece of research, reflecting the research process. It’s not an opinion piece , nor a place to push your agenda or try to convince someone of your position. Writing a good dissertation involves asking a question and taking a systematic, rigorous approach to answering it.
If you understand this and are comfortable leaving your opinions or preconceived ideas at the door, you’re already off to a good start!
Step 2: Find a unique, valuable research topic
As we saw, the first step of the research process is to ask a specific, well-articulated question. In other words, you need to find a research topic that asks a specific question or set of questions (these are called research questions ). Sounds easy enough, right? All you’ve got to do is identify a question or two and you’ve got a winning research topic. Well, not quite…
A good dissertation or thesis topic has a few important attributes. Specifically, a solid research topic should be:
Let’s take a closer look at these:
Attribute #1: Clear
Your research topic needs to be crystal clear about what you’re planning to research, what you want to know, and within what context. There shouldn’t be any ambiguity or vagueness about what you’ll research.
Here’s an example of a clearly articulated research topic:
An analysis of consumer-based factors influencing organisational trust in British low-cost online equity brokerage firms.
As you can see in the example, its crystal clear what will be analysed (factors impacting organisational trust), amongst who (consumers) and in what context (British low-cost equity brokerage firms, based online).
Need a helping hand?
Attribute #2: Unique
Your research should be asking a question(s) that hasn’t been asked before, or that hasn’t been asked in a specific context (for example, in a specific country or industry).
For example, sticking organisational trust topic above, it’s quite likely that organisational trust factors in the UK have been investigated before, but the context (online low-cost equity brokerages) could make this research unique. Therefore, the context makes this research original.
One caveat when using context as the basis for originality – you need to have a good reason to suspect that your findings in this context might be different from the existing research – otherwise, there’s no reason to warrant researching it.
Attribute #3: Important
Simply asking a unique or original question is not enough – the question needs to create value. In other words, successfully answering your research questions should provide some value to the field of research or the industry. You can’t research something just to satisfy your curiosity. It needs to make some form of contribution either to research or industry.
For example, researching the factors influencing consumer trust would create value by enabling businesses to tailor their operations and marketing to leverage factors that promote trust. In other words, it would have a clear benefit to industry.
So, how do you go about finding a unique and valuable research topic? We explain that in detail in this video post – How To Find A Research Topic . Yeah, we’ve got you covered 😊
Step 3: Write a convincing research proposal
Once you’ve pinned down a high-quality research topic, the next step is to convince your university to let you research it. No matter how awesome you think your topic is, it still needs to get the rubber stamp before you can move forward with your research. The research proposal is the tool you’ll use for this job.
So, what’s in a research proposal?
The main “job” of a research proposal is to convince your university, advisor or committee that your research topic is worthy of approval. But convince them of what? Well, this varies from university to university, but generally, they want to see that:
- You have a clearly articulated, unique and important topic (this might sound familiar…)
- You’ve done some initial reading of the existing literature relevant to your topic (i.e. a literature review)
- You have a provisional plan in terms of how you will collect data and analyse it (i.e. a methodology)
At the proposal stage, it’s (generally) not expected that you’ve extensively reviewed the existing literature , but you will need to show that you’ve done enough reading to identify a clear gap for original (unique) research. Similarly, they generally don’t expect that you have a rock-solid research methodology mapped out, but you should have an idea of whether you’ll be undertaking qualitative or quantitative analysis , and how you’ll collect your data (we’ll discuss this in more detail later).
Long story short – don’t stress about having every detail of your research meticulously thought out at the proposal stage – this will develop as you progress through your research. However, you do need to show that you’ve “done your homework” and that your research is worthy of approval .
So, how do you go about crafting a high-quality, convincing proposal? We cover that in detail in this video post – How To Write A Top-Class Research Proposal . We’ve also got a video walkthrough of two proposal examples here .
Step 4: Craft a strong introduction chapter
Once your proposal’s been approved, its time to get writing your actual dissertation or thesis! The good news is that if you put the time into crafting a high-quality proposal, you’ve already got a head start on your first three chapters – introduction, literature review and methodology – as you can use your proposal as the basis for these.
Handy sidenote – our free dissertation & thesis template is a great way to speed up your dissertation writing journey.
What’s the introduction chapter all about?
The purpose of the introduction chapter is to set the scene for your research (dare I say, to introduce it…) so that the reader understands what you’ll be researching and why it’s important. In other words, it covers the same ground as the research proposal in that it justifies your research topic.
What goes into the introduction chapter?
This can vary slightly between universities and degrees, but generally, the introduction chapter will include the following:
- A brief background to the study, explaining the overall area of research
- A problem statement , explaining what the problem is with the current state of research (in other words, where the knowledge gap exists)
- Your research questions – in other words, the specific questions your study will seek to answer (based on the knowledge gap)
- The significance of your study – in other words, why it’s important and how its findings will be useful in the world
As you can see, this all about explaining the “what” and the “why” of your research (as opposed to the “how”). So, your introduction chapter is basically the salesman of your study, “selling” your research to the first-time reader and (hopefully) getting them interested to read more.
How do I write the introduction chapter, you ask? We cover that in detail in this post .
Step 5: Undertake an in-depth literature review
As I mentioned earlier, you’ll need to do some initial review of the literature in Steps 2 and 3 to find your research gap and craft a convincing research proposal – but that’s just scratching the surface. Once you reach the literature review stage of your dissertation or thesis, you need to dig a lot deeper into the existing research and write up a comprehensive literature review chapter.
What’s the literature review all about?
There are two main stages in the literature review process:
Literature Review Step 1: Reading up
The first stage is for you to deep dive into the existing literature (journal articles, textbook chapters, industry reports, etc) to gain an in-depth understanding of the current state of research regarding your topic. While you don’t need to read every single article, you do need to ensure that you cover all literature that is related to your core research questions, and create a comprehensive catalogue of that literature , which you’ll use in the next step.
Reading and digesting all the relevant literature is a time consuming and intellectually demanding process. Many students underestimate just how much work goes into this step, so make sure that you allocate a good amount of time for this when planning out your research. Thankfully, there are ways to fast track the process – be sure to check out this article covering how to read journal articles quickly .
Literature Review Step 2: Writing up
Once you’ve worked through the literature and digested it all, you’ll need to write up your literature review chapter. Many students make the mistake of thinking that the literature review chapter is simply a summary of what other researchers have said. While this is partly true, a literature review is much more than just a summary. To pull off a good literature review chapter, you’ll need to achieve at least 3 things:
- You need to synthesise the existing research , not just summarise it. In other words, you need to show how different pieces of theory fit together, what’s agreed on by researchers, what’s not.
- You need to highlight a research gap that your research is going to fill. In other words, you’ve got to outline the problem so that your research topic can provide a solution.
- You need to use the existing research to inform your methodology and approach to your own research design. For example, you might use questions or Likert scales from previous studies in your your own survey design .
As you can see, a good literature review is more than just a summary of the published research. It’s the foundation on which your own research is built, so it deserves a lot of love and attention. Take the time to craft a comprehensive literature review with a suitable structure .
But, how do I actually write the literature review chapter, you ask? We cover that in detail in this video post .
Step 6: Carry out your own research
Once you’ve completed your literature review and have a sound understanding of the existing research, its time to develop your own research (finally!). You’ll design this research specifically so that you can find the answers to your unique research question.
There are two steps here – designing your research strategy and executing on it:
1 – Design your research strategy
The first step is to design your research strategy and craft a methodology chapter . I won’t get into the technicalities of the methodology chapter here, but in simple terms, this chapter is about explaining the “how” of your research. If you recall, the introduction and literature review chapters discussed the “what” and the “why”, so it makes sense that the next point to cover is the “how” –that’s what the methodology chapter is all about.
In this section, you’ll need to make firm decisions about your research design. This includes things like:
- Your research philosophy (e.g. positivism or interpretivism )
- Your overall methodology (e.g. qualitative , quantitative or mixed methods)
- Your data collection strategy (e.g. interviews , focus groups, surveys)
- Your data analysis strategy (e.g. content analysis , correlation analysis, regression)
If these words have got your head spinning, don’t worry! We’ll explain these in plain language in other posts. It’s not essential that you understand the intricacies of research design (yet!). The key takeaway here is that you’ll need to make decisions about how you’ll design your own research, and you’ll need to describe (and justify) your decisions in your methodology chapter.
2 – Execute: Collect and analyse your data
Once you’ve worked out your research design, you’ll put it into action and start collecting your data. This might mean undertaking interviews, hosting an online survey or any other data collection method. Data collection can take quite a bit of time (especially if you host in-person interviews), so be sure to factor sufficient time into your project plan for this. Oftentimes, things don’t go 100% to plan (for example, you don’t get as many survey responses as you hoped for), so bake a little extra time into your budget here.
Once you’ve collected your data, you’ll need to do some data preparation before you can sink your teeth into the analysis. For example:
- If you carry out interviews or focus groups, you’ll need to transcribe your audio data to text (i.e. a Word document).
- If you collect quantitative survey data, you’ll need to clean up your data and get it into the right format for whichever analysis software you use (for example, SPSS, R or STATA).
Once you’ve completed your data prep, you’ll undertake your analysis, using the techniques that you described in your methodology. Depending on what you find in your analysis, you might also do some additional forms of analysis that you hadn’t planned for. For example, you might see something in the data that raises new questions or that requires clarification with further analysis.
The type(s) of analysis that you’ll use depend entirely on the nature of your research and your research questions. For example:
- If your research if exploratory in nature, you’ll often use qualitative analysis techniques .
- If your research is confirmatory in nature, you’ll often use quantitative analysis techniques
- If your research involves a mix of both, you might use a mixed methods approach
Again, if these words have got your head spinning, don’t worry! We’ll explain these concepts and techniques in other posts. The key takeaway is simply that there’s no “one size fits all” for research design and methodology – it all depends on your topic, your research questions and your data. So, don’t be surprised if your study colleagues take a completely different approach to yours.
Step 7: Present your findings
Once you’ve completed your analysis, it’s time to present your findings (finally!). In a dissertation or thesis, you’ll typically present your findings in two chapters – the results chapter and the discussion chapter .
What’s the difference between the results chapter and the discussion chapter?
While these two chapters are similar, the results chapter generally just presents the processed data neatly and clearly without interpretation, while the discussion chapter explains the story the data are telling – in other words, it provides your interpretation of the results.
For example, if you were researching the factors that influence consumer trust, you might have used a quantitative approach to identify the relationship between potential factors (e.g. perceived integrity and competence of the organisation) and consumer trust. In this case:
- Your results chapter would just present the results of the statistical tests. For example, correlation results or differences between groups. In other words, the processed numbers.
- Your discussion chapter would explain what the numbers mean in relation to your research question(s). For example, Factor 1 has a weak relationship with consumer trust, while Factor 2 has a strong relationship.
Depending on the university and degree, these two chapters (results and discussion) are sometimes merged into one , so be sure to check with your institution what their preference is. Regardless of the chapter structure, this section is about presenting the findings of your research in a clear, easy to understand fashion.
Importantly, your discussion here needs to link back to your research questions (which you outlined in the introduction or literature review chapter). In other words, it needs to answer the key questions you asked (or at least attempt to answer them).
For example, if we look at the sample research topic:
In this case, the discussion section would clearly outline which factors seem to have a noteworthy influence on organisational trust. By doing so, they are answering the overarching question and fulfilling the purpose of the research .
For more information about the results chapter , check out this post for qualitative studies and this post for quantitative studies .
Step 8: The Final Step Draw a conclusion and discuss the implications
Last but not least, you’ll need to wrap up your research with the conclusion chapter . In this chapter, you’ll bring your research full circle by highlighting the key findings of your study and explaining what the implications of these findings are.
What exactly are key findings? The key findings are those findings which directly relate to your original research questions and overall research objectives (which you discussed in your introduction chapter). The implications, on the other hand, explain what your findings mean for industry, or for research in your area.
Sticking with the consumer trust topic example, the conclusion might look something like this:
Key findings
This study set out to identify which factors influence consumer-based trust in British low-cost online equity brokerage firms. The results suggest that the following factors have a large impact on consumer trust:
While the following factors have a very limited impact on consumer trust:
Notably, within the 25-30 age groups, Factors E had a noticeably larger impact, which may be explained by…
Implications
The findings having noteworthy implications for British low-cost online equity brokers. Specifically:
The large impact of Factors X and Y implies that brokers need to consider….
The limited impact of Factor E implies that brokers need to…
As you can see, the conclusion chapter is basically explaining the “what” (what your study found) and the “so what?” (what the findings mean for the industry or research). This brings the study full circle and closes off the document.
Let’s recap – how to write a dissertation or thesis
You’re still with me? Impressive! I know that this post was a long one, but hopefully you’ve learnt a thing or two about how to write a dissertation or thesis, and are now better equipped to start your own research.
To recap, the 8 steps to writing a quality dissertation (or thesis) are as follows:
- Understand what a dissertation (or thesis) is – a research project that follows the research process.
- Find a unique (original) and important research topic
- Craft a convincing dissertation or thesis research proposal
- Write a clear, compelling introduction chapter
- Undertake a thorough review of the existing research and write up a literature review
- Undertake your own research
- Present and interpret your findings
Once you’ve wrapped up the core chapters, all that’s typically left is the abstract , reference list and appendices. As always, be sure to check with your university if they have any additional requirements in terms of structure or content.
Psst... there’s more!
This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...
20 Comments
thankfull >>>this is very useful
Thank you, it was really helpful
unquestionably, this amazing simplified way of teaching. Really , I couldn’t find in the literature words that fully explicit my great thanks to you. However, I could only say thanks a-lot.
Great to hear that – thanks for the feedback. Good luck writing your dissertation/thesis.
This is the most comprehensive explanation of how to write a dissertation. Many thanks for sharing it free of charge.
Very rich presentation. Thank you
Thanks Derek Jansen|GRADCOACH, I find it very useful guide to arrange my activities and proceed to research!
Thank you so much for such a marvelous teaching .I am so convinced that am going to write a comprehensive and a distinct masters dissertation
It is an amazing comprehensive explanation
This was straightforward. Thank you!
I can say that your explanations are simple and enlightening – understanding what you have done here is easy for me. Could you write more about the different types of research methods specific to the three methodologies: quan, qual and MM. I look forward to interacting with this website more in the future.
Thanks for the feedback and suggestions 🙂
Hello, your write ups is quite educative. However, l have challenges in going about my research questions which is below; *Building the enablers of organisational growth through effective governance and purposeful leadership.*
Very educating.
Just listening to the name of the dissertation makes the student nervous. As writing a top-quality dissertation is a difficult task as it is a lengthy topic, requires a lot of research and understanding and is usually around 10,000 to 15000 words. Sometimes due to studies, unbalanced workload or lack of research and writing skill students look for dissertation submission from professional writers.
Thank you 💕😊 very much. I was confused but your comprehensive explanation has cleared my doubts of ever presenting a good thesis. Thank you.
thank you so much, that was so useful
Hi. Where is the excel spread sheet ark?
could you please help me look at your thesis paper to enable me to do the portion that has to do with the specification
my topic is “the impact of domestic revenue mobilization.
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Is it normal in your field for a PhD thesis to be less than 100 pages?
The length of a PhD thesis largely depends on the academic discipline and specific requirements of the institution. In the humanities or social sciences, theses often exceed 250 pages because of the extensive qualitative data and literature reviews. Is it normal in your field or subfield for a PhD thesis to be less than 100 pages?
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Dissertations
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Introduction to Dissertation
OMMS and Part C students are required to undertake a dissertation worth two units as part of their degree programme. This can be either a mathematics dissertation or a statistics dissertation.
The dissertation will entail investigating a topic in an area of the Mathematical Sciences under the guidance of a dissertation supervisor. This will culminate in a written dissertation with a word limit of 7,500 words, which usually equates to 25-35 pages. It is expected that students embarking on a dissertation will be working on it over Christmas vacation, Hilary Term and Easter vacation for submission in early Trinity Term.
Students completing a dissertation may request a book for consultation if it is held only by the Whitehead Library (and not held in the RSL, their College library or as an e-book) by emailing the Librarian at @email .
The book will be sent to the RSL where it can be consulted for reference, not borrowing. Please see further information here .
Timetable for Dissertations
Week 0, Friday | Dissertation Information Session |
Week 0-1 | Dissertation abstracts published |
Week 3, Friday 12:00 | Deadline for submitting dissertation choices |
Week 5, Friday | Students notified of project allocation |
Weeks 7 and 8 | 1-2 initial meetings with dissertation supervisor |
Weeks 1-8 | 4 or 5 further supervision meetings |
Weeks 7 and 8 | Oral presentations take place |
Week 1, Monday 12:00 | Submission deadline |
Choosing a topic
Following the Dissertation Information Session, a list of potential dissertation topics will be published below. Each topic will be accompanied by a short abstract outlining the project with details on necessary pre-requisite knowledge and the maximum number of students who will be able to take each topic. You will be asked to complete an online form, ranking 5 of the topics. Please note that Maths Part C students are only permitted to chose a maximum of three statistics topics. You will be notified of which project you have been allocated by the end of week 5.
Oral Presentation
Each student is required to give an oral presentation to their supervisors and at least one other person with some knowledge of the field of the dissertation. These will usually take place in the final two weeks of Hilary Term. The presentation does not count towards the final assessment of the project, however, it will give you an opportunity to practise your presentation skills which will prove useful in your later careers.
Useful Links and Sources of Information
- Nov 2022 Dissertations Information Session
- Dissertation_Guidenotes_2023-24.pdf
- Past project archive
- Mathematical Institute's LaTeX help
- University guidance on research and library skills
- University guidance on referencing
- oral_presentation_guidelines_2023-24.pdf
- Guidance for Supervisors 2023-24_1.pdf
The First Notices to Candidates (including information on dissertations) can be found here .
IMAGES
VIDEO
COMMENTS
What is the shortest Ph.D. thesis? [closed]
When John Nash wrote "Non Cooperative Games," his Ph.D. dissertation at Princeton in 1950, the text of his thesis (read it online) was brief. It ran only 26 pages. And more particularly, it was light on citations. Nash's diss cited two texts: John von Neumann & Oskar Morgenstern's Theory of Games ...
16 pages - Edmund Landau: Neuer Beweis der Gleichung (1899) / New Proof of the Equation (2007) 13 pages - Burt Totaro: Milnor K-Theory is the Simplest Part of Algebraic K-Theory (1992) 9 pages - David Lee Rector: An Unstable Adams Spectral Sequence (1966) Please drop us a line if you know any shorter dissertations than the ones above!
Math can be hard and tedious resulting in very long papers. The 1995 proof of Fermat's last Theorem was 108 pages long. But math can also be short. Lander and Parkin's paper about a conjecture by Euler (related to Fermat's last Theorem), is probably the dream of everyone ever written a paper: It answers an interesting and important ...
I am looking for short papers that made a significant impact on the mathematics community. I have already seen: interesting-but-short-math-papers and, What is the Shortest Ph.D. Thesis? on math overflow, but these weren't quite what I was looking for (although the intersection of the set of answers to this question with the set of answers to either of the above links is likely to be non-trivial)
Nash earned a Ph.D. degree in 1950 with a 28-page dissertation on non-cooperative games. The thesis, written under the supervision of doctoral advisor Albert W. Tucker, contained the definition and properties of the Nash equilibrium, a crucial concept in non-cooperative games. It won Nash the Nobel Memorial Prize in Economic Sciences in 1994.
The shortest possible do ctoral thesis in mathematics has no sentenc es at all. As a way of a proof we giv e the celebrated example of Euler's discovery of the composite character of the number ...
Economics, mathematics, and biostatistics had the lowest median page lengths, whereas anthropology, history, and political science had the highest median page lengths. This distinction makes sense given the nature of the disciplines. I was on the long end of the statistics distribution, around 180 pages. Probably because I had a lot of pictures.
Department of Mathematics, California State University-Los Angeles, 5151 State University Drive, Los Angeles, CA 90032 [email protected]. A Refinement of a Theorem of J. E. LittlewoodIn [1], J. E. Littlewood raises the question of how short a doctoral dissertation in mathematics could in principle be,1 and propose.
Harvard Department of Mathematics PhD Dissertations ...
It could also be helpful to check this and this short guides and the books by Steven G. Krantz, in particular. A Mathematician's Survival Guide: Graduate School and Early Career Development. A Primer of Mathematical Writing. The first one contains subsection 4.6 which deals specifically with writing a thesis, the second one is on mathematical ...
Many older dissertations can be found on ProQuest Dissertation and Theses Search which many university libraries subscribe to. Harvard University. Department of Mathematics. Science Center Room 325. 1 Oxford Street. Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main Office Contact.
Dissertations and Placements 2010-Present - Cornell Math
How long is a PhD dissertation? [Data by field]
A math dissertation might as well be Martian with all the symbols. A lot of humanities dissertations might as well be Martian because of all the theory being used which necessitates an esoteric vocabulary. Read a page of Bertrand Russell's stuff on philosophy of language or Heidegger's stuff on phenomenology and, for a person outside the ...
PhD Dissertations | Department of Mathematics - OSU Math
Mathematics Theses, Projects, and Dissertations
9. I think this varies a lot. But for Germany your first question can be answers succinctly: In a Master's thesis you should show that you have potential for research. On the other hand, expectations vary a lot between advisors. But certainly you do not have to prove a new theorem or develop a new theory.
How To Write A Dissertation Or Thesis (+ Examples)
DEPARTMENT OF MATHEMATICS. The graduate faculty in the Department of Mathematics agrees with the principles in the newly adopted Graduate School-New Brunswick's GUIDELINES ON TIME FOR REVIEW AND ASSESSMENT OF QUALIFYING PAPERS, THESES AND DISSERTATIONS": to maintain a culture of mutual respect between students and faculty members and that this include excellent communication among them.
The shortest thesis I ever saw was like 75 pages, but that student had... issues. They were basically allowed to leave with a PhD, but didn't actually take up a career that needed it. It's much more usual for the thesis to be 200-300 pages. ... My dad's PhD thesis in mathematics was 20 pages, he became a full professor at 29. My master thesis ...
This can be either a mathematics dissertation or a statistics dissertation. ... Each topic will be accompanied by a short abstract outlining the project with details on necessary pre-requisite knowledge and the maximum number of students who will be able to take each topic. You will be asked to complete an online form, ranking 5 of the topics.
Shortest Mathematics Phd Thesis - Free download as PDF File (.pdf), Text File (.txt) or read online for free. - Writing a mathematics PhD thesis can be an incredibly challenging and time-consuming task that requires precision and dedication, from conducting extensive research to analyzing data and formulating arguments. - For many students, the pressure of producing a high-quality thesis while ...