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Phi Beta Kappa Inducts 54 Mathematics Seniors

The Xi Chapter of Phi Beta Kappa has elected 54 mathematics majors, among 127 electees from MIT's Class of 2024, to become members.

Founded in 1776, Phi Beta Kappa is the nation’s oldest academic honor society. Membership is awarded to students in recognition of excellent academic records and commitment to the objectives of a liberal education. The annual Phi Beta Kappa lecture and initiation ceremony is May 29, during MIT’s Commencement week.

Full list of Mathematics Inductees

Congratulations to our newest members of Phi Beta Kappa!

Ben Lou and Kenta Suzuki Receive Goldwater Scholarships

Ben is majoring in physics and math with a minor in philosophy. Under the mentorship of the LIGO Group’s Nergis Mavalvala, dean of the School of Science, and graduate student Hudson Loughlin, he is working on research to advance the field of quantum measurement, with potential applications including quantum gravity. He thanks his advisors Janet Conrad from Physics and Thomas Rüd from Math. He also acknowledges support from Math’s Elijah Bodish and Roman Bezrukavnikov ; Physics’ Alan Guth, Barton Zwiebach, and Richard Price; and David W. Brown of the San Diego Math Circle.

An alum of the PRIMES and SPUR programs, Kenta is a math major who works with Roman on research at the intersection of number and representation theory, using geometric methods to represent p-adic groups. Kenta says he was also inspired to research representation theory by Zhiwei Yun and Wei Zhang .

They were among 438 U.S. college students selected on the basis of academic merit.

Congratulations, Ben and Kenta!

Read more in the MIT News .

Dor Minzer and Kai Zhe Zheng to Receive STOC 2024 Best Paper Award

Assistant Professor Dor Minzer and graduate student Kai Zhe Zheng will be receiving a Best Paper Award at the June 24-28 Association for Computing Machinery (ACM) Symposium on Theory of Computing (STOC 2024).

In their paper, Dor and Kai provide a near-optimal trade-off for so-called 2-prover 1-round games, which are crucial to proving strong inapproximability results.

Dor and others from our Department and MIT have other papers that have been accepted at the symposium. The symposium is the flagship conference of ACM’s SIGACT (Special Interest Group on Algorithms and Computation Theory).

Congratulations, Dor and Kai!

Andre Lee Dixon Selected for School of Science Infinite Mile Award

The School of Science has selected Mathematics Program Coordinator André Lee Dixon as one of the recipients of the 2024 Infinite Mile Award !

“I have been consistently struck by the level of initiative and passion André brings to work,” says his nominator, John Urschel PhD ’21.

Infinite Mile Award winners are nominated by colleagues for going above and beyond in their roles at the Institute.

Congratulations, André!

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Mit alumnus and professor are awarded nobel honors.

• Oct 13, 2021
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Two members of the MIT community won 2021 Nobel Prizes in different categories: alumnus David Julius ’77, who shares the Nobel Prize in Physiology or Medicine, and Joshua Angrist, who shares the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.

Julius, a professor at the University of California at San Francisco, is at least the 38th Nobel laureate to hold a degree from MIT (see the full list at the end of this story), sharing the prize with Ardem Patapoutian, a professor at the Scripps Research Institute, for their discoveries in how the body senses touch and temperature. The pair “utilized capsaicin, a pungent compound from chili peppers that induces a burning sensation, to identify a sensor in the nerve endings of the skin that responds to heat,” the Nobel committee said in a news release . “The laureates identified critical missing links in our understanding of the complex interplay between our senses and the environment.”

Julius majored in biology at MIT as an undergraduate before earning a PhD in 1984 from University of California at Berkeley and was a postdoc at Columbia University. Read more on MIT News .

Angrist, an MIT labor economist, is recognized for his influential work enhancing rigorous empirical research and establishing new methods of conducting “natural experiments” in economics. He shares the prize with David Card of the University of California at Berkeley and Guido Imbens of Stanford Graduate School of Business, and brings the tally of MIT alumni to receive a Nobel Prize to 39. “Their research has substantially improved our ability to answer key causal questions, which has been of great benefit to society,” the Nobel committee said in a news release . Read more on MIT News .

Julius and Angrist bring the total MIT-connected Nobel winners to 98.  Visit MIT’s Institutional Research Page for more details , and see the MIT Alumni laureates below.  

Top photo (left to right): David Julius ’77 (Photo credit: Steve Babuljak, UCSF) and Joshua Angrist (Photo credit: Lillie Paquette). 

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Teri Centner

Thu, 10/14/2021 4:39pm

Nobel Prize Infographic

Is there an accessible version of the infographic? (Or perhaps a downloadable CSV file or spreadsheet?)

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Doctoral Degrees

A doctoral degree requires the satisfactory completion of an approved program of advanced study and original research of high quality..

Please note that the Doctor of Philosophy (PhD) and Doctor of Science (ScD) degrees are awarded interchangeably by all departments in the School of Engineering and the School of Science, except in the fields of biology, cognitive science, neuroscience, medical engineering, and medical physics. This means that, excepting the departments outlined above, the coursework and expectations to earn a Doctor of Philosophy and for a Doctor of Science degree from these schools are generally the same. Doctoral students may choose which degree they wish to complete.

Applicants interested in graduate education should apply to the department or graduate program conducting research in the area of interest. Some departments require a doctoral candidate to take a “minor” program outside of the student’s principal field of study; if you wish to apply to one of these departments, please consider additional fields you may like to pursue.

Below is a list of programs and departments that offer doctoral-level degrees.

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PhD Program

Program overview.

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Rigorous, discipline-based research is the hallmark of the MIT Sloan PhD Program. The program is committed to educating scholars who will lead in their fields of research—those with outstanding intellectual skills who will carry forward productive research on the complex organizational, financial, and technological issues that characterize an increasingly competitive and challenging business world.

Start here.

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Click here for answers to many of the most frequently asked questions.

PhD studies at MIT Sloan are intense and individual in nature, demanding a great deal of time, initiative, and discipline from every candidate. But the rewards of such rigor are tremendous:  MIT Sloan PhD graduates go on to teach and conduct research at the world's most prestigious universities.

PhD Program curriculum at MIT Sloan is organized under the following three academic areas: Behavior & Policy Sciences; Economics, Finance & Accounting; and Management Science. Our nine research groups correspond with one of the academic areas, as noted below.

MIT Sloan PhD Research Groups

Behavioral & policy sciences.

Economic Sociology

Institute for Work & Employment Research

Organization Studies

Technological Innovation, Entrepreneurship & Strategic Management

Economics, Finance & Accounting

Accounting  

Management Science

Information Technology

System Dynamics  

Those interested in a PhD in Operations Research should visit the Operations Research Center .  

PhD Program Structure

Additional information including coursework and thesis requirements.

MIT Sloan Predoctoral Opportunities

MIT Sloan is eager to provide a diverse group of talented students with early-career exposure to research techniques as well as support in considering research career paths.

Rising Scholars Conference

The fourth annual Rising Scholars Conference on October 25 and 26 gathers diverse PhD students from across the country to present their research.

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The goal of the MIT Sloan PhD Program's admissions process is to select a small number of people who are most likely to successfully complete our rigorous and demanding program and then thrive in academic research careers. The admission selection process is highly competitive; we aim for a class size of nineteen students, admitted from a pool of hundreds of applicants.

What We Seek

• Outstanding intellectual ability
• Excellent academic records
• Previous work in disciplines related to the intended area of concentration
• Strong commitment to a career in research

MIT Sloan PhD Program Admissions Requirements Common Questions

Dates and Deadlines

Admissions for 2024 is closed. The next opportunity to apply will be for 2025 admission. The 2025 application will open in September 2024. 

More information on program requirements and application components

Students in good academic standing in our program receive a funding package that includes tuition, medical insurance, and a fellowship stipend and/or TA/RA salary. We also provide a new laptop computer and a conference travel/research budget.

Funding Information

Throughout the year, we organize events that give you a chance to learn more about the program and determine if a PhD in Management is right for you.

PhD Program Events

June phd program overview.

During this webinar, you will hear from the PhD Program team and have the chance to ask questions about the application and admissions process.

July PhD Program Overview

August phd program overview, september 12 phd program overview.

Complete PhD Admissions Event Calendar

Unlike formulaic approaches to training scholars, the PhD Program at MIT Sloan allows students to choose their own adventure and develop a unique scholarly identity. This can be daunting, but students are given a wide range of support along the way - most notably having access to world class faculty and coursework both at MIT and in the broader academic community around Boston.

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Profiles of our current students

MIT Sloan produces top-notch PhDs in management. Immersed in MIT Sloan's distinctive culture, upcoming graduates are poised to innovate in management research and education. Here are the academic placements for our PhDs graduating in May and September 2024. Our 2024-2025 job market candidates will be posted in early June 2024.

Academic Job Market

Doctoral candidates on the current academic market

Academic Placements

Graduates of the MIT Sloan PhD Program are researching and teaching at top schools around the world.

view recent placements 

MIT Sloan Experience

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The PhD Program is integral to the research of MIT Sloan's world-class faculty. With a reputation as risk-takers who are unafraid to embrace the unconventional, they are engaged in exciting disciplinary and interdisciplinary research that often includes PhD students as key team members.

Research centers across MIT Sloan and MIT provide a rich setting for collaboration and exploration. In addition to exposure to the faculty, PhD students also learn from one another in a creative, supportive research community.

Throughout MIT Sloan's history, our professors have devised theories and fields of study that have had a profound impact on management theory and practice.

From Douglas McGregor's Theory X/Theory Y distinction to Nobel-recognized breakthroughs in finance by Franco Modigliani and in option pricing by Robert Merton and Myron Scholes, MIT Sloan's faculty have been unmatched innovators.

This legacy of innovative thinking and dedication to research impacts every faculty member and filters down to the students who work beside them.

Faculty Links

• Accounting Faculty
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Student Research

“MIT Sloan PhD training is a transformative experience. The heart of the process is the student’s transition from being a consumer of knowledge to being a producer of knowledge. This involves learning to ask precise, tractable questions and addressing them with creativity and rigor. Hard work is required, but the reward is the incomparable exhilaration one feels from having solved a puzzle that had bedeviled the sharpest minds in the world!” -Ezra Zuckerman Sivan Alvin J. Siteman (1948) Professor of Entrepreneurship

Sample Dissertation Abstracts - These sample Dissertation Abstracts provide examples of the work that our students have chosen to study while in the MIT Sloan PhD Program.

We believe that our doctoral program is the heart of MIT Sloan's research community and that it develops some of the best management researchers in the world. At our annual Doctoral Research Forum, we celebrate the great research that our doctoral students do, and the research community that supports that development process.

The videos of their presentations below showcase the work of our students and will give you insight into the topics they choose to research in the program.

Attention To Retention: The Informativeness of Insiders’ Decision to Retain Shares

2024 PhD Doctoral Research Forum Winner - Gabriel Voelcker

Watch more MIT Sloan PhD Program  Doctoral Forum Videos

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Associate Professor of Mathematics Department of Mathematics Massachusetts Institute of Technology

Office: 2-271

Mail: MIT Department of Mathematics 77 Massachusetts Ave, Bldg 2-271 Cambridge, MA 02139, USA

Research Interests: Combinatorics

• Extremal, probabilistic, and additive combinatorics
• Graph theory; discrete geometry; applications to computer science

Current PhD Students : Travis Dillon , Dingding Dong , Nitya Mani , Ashwin Sah , Mehtaab Sawhney

Former PhD Students : Benjamin Gunby , Jonathan Tidor , Aaron Berger

Co-organizer, Richard P. Stanley Seminar in Combinatorics

Editorial: Advances in Mathematics , Research in the Mathematical Sciences , Springer Graduate Texts in Mathematics

(Book) Graph Theory and Additive Combinatorics: Exploring Structure and Randomness

Cambridge University Press 2023

Lecture videos on MIT OpenCourseWare and YouTube

(Lecture Notes) Probabilistic Methods in Combinatorics

• 18.225 Graph Theory and Additive Combinatorics (grad), Fall 2023 Book Exercises MIT OCW YouTube
• 18.226 Probabilistic Methods in Combinatorics (grad), Fall 2022 Notes Exercises
• 18.211 Combinatorial Analysis , Fall 2018
• Polynomial Method in Combinatorics (grad), Trinity Term 2016, Oxford
• Math Olympiad training handouts

Selected papers

• Nearly all $k$-SAT functions are unate (with József Balogh, Dingding Dong, Bernard Lidický, and Nitya Mani) ACM Symposium on Theory of Computing (STOC 2023)
• Joints of varieties (with Jonathan Tidor and Hung-Hsun Hans Yu) Geometric and Functional Analysis 32 (2022) 302–339
• Testing linear-invariant properties (with Jonathan Tidor) IEEE Symposium on Foundations of Computer Science (FOCS) 2020 SIAM Journal on Computing 51 (2022), 1230–1279
• Equiangular lines with a fixed angle (with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang) Annals of Mathematics 194 (2021), 729–743. MIT News
• A reverse Sidorenko inequality (with Ashwin Sah, Mehtaab Sawhney, and David Stoner) Inventiones Mathematicae 221 (2020), 665–711
• Upper tails and independence polynomials in random graphs (with Bhaswar B. Bhattacharya, Shirshendu Ganguly, and Eyal Lubetzky) Advances in Mathematics 319 (2017), 313–347
• A relative Szemerédi theorem (with David Conlon and Jacob Fox) Geometric and Functional Analysis 25 (2015), 733–762
• Sphere packing bounds via spherical codes (with Henry Cohn) Duke Mathematical Journal 163 (2014), 1965–2002
• Equiangular lines and eigenvalue multiplicities
• Extremal problems in discrete geometry
• The joints problem for varieties
• Popular common difference
• Regularity method for sparse graphs and its applications
• A reverse Sidorenko inequality: independent sets, colorings, and graph homomorphisms
• Large deviations in random graphs
• Pseudorandom graphs, relative Szemerédi theorem and the Green-Tao Theorem
• Nearly all k -SAT functions are unate , Simons Institute, Berkeley, Jul 2023
• Uniform sets with few progressions via colorings , IAS, May 2023
• Equiangular lines and eigenvalue multiplicities , Waterloo Algebraic Graph Theory Seminar, Aug 2022
• The joints problem for varieties , Big Seminar by Laboratory of Combinatorial and Geometric Structures, Aug 2020
• Popular common difference , Webinar in Additive Combinatorics, May 2020
• Equiangular lines with a fixed angle , Banff International Research Station, Sep 2019
• Large deviations and exponential random graphs , Northeastern University Network Science Institute, May 2018
• Sparse graph regularity tutorial , Simons Institute, Berkeley, Jan 2017
• Green–Tao theorem and a relative Szemerédi theorem , Simons Institute, Berkeley, Dec 2013

Also see Youtube playlist for more videos

• NSF CAREER award, 2021
• Sloan Research Fellowship , 2019
• Dénes König Prize , 2018
• Ph.D. Mathematics, MIT, 2015 (Advisor: Jacob Fox )
• M.A.St. Mathematics with Distinction, Cambridge, 2011
• S.B. Mathematics, MIT, 2010
• S.B. Computer Science and Engineering, MIT, 2010
• Previous affiliations: Oxford, Berkeley, Stanford, Microsoft Research

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Elaine Liu: Charging ahead

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MIT senior Elaine Siyu Liu doesn’t own an electric car, or any car. But she sees the impact of electric vehicles (EVs) and renewables on the grid as two pieces of an energy puzzle she wants to solve.

The U.S. Department of Energy reports that the number of public and private EV charging ports nearly doubled in the past three years, and many more are in the works. Users expect to plug in at their convenience, charge up, and drive away. But what if the grid can’t handle it?

Electricity demand, long stagnant in the United States, has spiked due to EVs, data centers that drive artificial intelligence, and industry. Grid planners forecast an increase of 2.6 percent to 4.7 percent in electricity demand over the next five years, according to data reported to federal regulators. Everyone from EV charging-station operators to utility-system operators needs help navigating a system in flux.

That’s where Liu’s work comes in.

Liu, who is studying mathematics and electrical engineering and computer science (EECS), is interested in distribution — how to get electricity from a centralized location to consumers. “I see power systems as a good venue for theoretical research as an application tool,” she says. “I'm interested in it because I'm familiar with the optimization and probability techniques used to map this level of problem.”

Liu grew up in Beijing, then after middle school moved with her parents to Canada and enrolled in a prep school in Oakville, Ontario, 30 miles outside Toronto.

Liu stumbled upon an opportunity to take part in a regional math competition and eventually started a math club, but at the time, the school’s culture surrounding math surprised her. Being exposed to what seemed to be some students’ aversion to math, she says, “I don’t think my feelings about math changed. I think my feelings about how people feel about math changed.”

Liu brought her passion for math to MIT. The summer after her sophomore year, she took on the first of the two Undergraduate Research Opportunity Program projects she completed with electric power system expert Marija Ilić, a joint adjunct professor in EECS and a senior research scientist at the MIT Laboratory for Information and Decision Systems.

Predicting the grid

Since 2022, with the help of funding from the MIT Energy Initiative (MITEI), Liu has been working with Ilić on identifying ways in which the grid is challenged.

One factor is the addition of renewables to the energy pipeline. A gap in wind or sun might cause a lag in power generation. If this lag occurs during peak demand, it could mean trouble for a grid already taxed by extreme weather and other unforeseen events.

If you think of the grid as a network of dozens of interconnected parts, once an element in the network fails — say, a tree downs a transmission line — the electricity that used to go through that line needs to be rerouted. This may overload other lines, creating what’s known as a cascade failure.

“This all happens really quickly and has very large downstream effects,” Liu says. “Millions of people will have instant blackouts.”

Even if the system can handle a single downed line, Liu notes that “the nuance is that there are now a lot of renewables, and renewables are less predictable. You can't predict a gap in wind or sun. When such things happen, there’s suddenly not enough generation and too much demand. So the same kind of failure would happen, but on a larger and more uncontrollable scale.”

Renewables’ varying output has the added complication of causing voltage fluctuations. “We plug in our devices expecting a voltage of 110, but because of oscillations, you will never get exactly 110,” Liu says. “So even when you can deliver enough electricity, if you can't deliver it at the specific voltage level that is required, that’s a problem.”

Liu and Ilić are building a model to predict how and when the grid might fail. Lacking access to privatized data, Liu runs her models with European industry data and test cases made available to universities. “I have a fake power grid that I run my experiments on,” she says. “You can take the same tool and run it on the real power grid.”

Liu’s model predicts cascade failures as they evolve. Supply from a wind generator, for example, might drop precipitously over the course of an hour. The model analyzes which substations and which households will be affected. “After we know we need to do something, this prediction tool can enable system operators to strategically intervene ahead of time,” Liu says.

Dictating price and power

Last year, Liu turned her attention to EVs, which provide a different kind of challenge than renewables.

In 2022, S&P Global reported that lawmakers argued that the U.S. Federal Energy Regulatory Commission’s (FERC) wholesale power rate structure was unfair for EV charging station operators.

In addition to operators paying by the kilowatt-hour, some also pay more for electricity during peak demand hours. Only a few EVs charging up during those hours could result in higher costs for the operator even if their overall energy use is low.

Anticipating how much power EVs will need is more complex than predicting energy needed for, say, heating and cooling. Unlike buildings, EVs move around, making it difficult to predict energy consumption at any given time. “If users don't like the price at one charging station or how long the line is, they'll go somewhere else,” Liu says. “Where to allocate EV chargers is a problem that a lot of people are dealing with right now.”

One approach would be for FERC to dictate to EV users when and where to charge and what price they'll pay. To Liu, this isn’t an attractive option. “No one likes to be told what to do,” she says.

Liu is looking at optimizing a market-based solution that would be acceptable to top-level energy producers — wind and solar farms and nuclear plants — all the way down to the municipal aggregators that secure electricity at competitive rates and oversee distribution to the consumer.

Analyzing the location, movement, and behavior patterns of all the EVs driven daily in Boston and other major energy hubs, she notes, could help demand aggregators determine where to place EV chargers and how much to charge consumers, akin to Walmart deciding how much to mark up wholesale eggs in different markets.

Last year, Liu presented the work at MITEI’s annual research conference. This spring, Liu and Ilić are submitting a paper on the market optimization analysis to a journal of the Institute of Electrical and Electronics Engineers.

Liu has come to terms with her early introduction to attitudes toward STEM that struck her as markedly different from those in China. She says, “I think the (prep) school had a very strong ‘math is for nerds’ vibe, especially for girls. There was a ‘why are you giving yourself more work?’ kind of mentality. But over time, I just learned to disregard that.”

After graduation, Liu, the only undergraduate researcher in Ilić’s MIT Electric Energy Systems Group, plans to apply to fellowships and graduate programs in EECS, applied math, and operations research.

Based on her analysis, Liu says that the market could effectively determine the price and availability of charging stations. Offering incentives for EV owners to charge during the day instead of at night when demand is high could help avoid grid overload and prevent extra costs to operators. “People would still retain the ability to go to a different charging station if they chose to,” she says. “I'm arguing that this works.”

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Related links.

• Electric Energy Systems Group
• MIT Energy Initiative
• Department of Electrical Engineering and Computer Science
• Department of Mathematics

Related Topics

• Electrical engineering and computer science (EECS)
• Mathematics
• Laboratory for Information and Decision Systems (LIDS)
• Undergraduate Research Opportunities Program (UROP)
• Renewable energy
• Electricity
• Electric vehicles
• Undergraduate

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