Associate Professor of Mathematics
Department of Mathematics
Massachusetts Institute of Technology
Email:
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: Aaron Berger, Travis Dillon, Dingding Dong, Nitya Mani, Ashwin Sah, Mehtaab Sawhney
Former PhD Students: Benjamin Gunby, Jonathan Tidor
See my blog for discussions of recent research
Co-organizer, Richard P. Stanley Seminar in Combinatorics
Associate Editor, Advances in Mathematics
Editorial Advisory Board Member, Springer Graduate Texts in Mathematics
(Book) Graph Theory and Additive Combinatorics: Exploring Structure and Randomness
To be published by Cambridge University Press
Lecture videos on MIT OpenCourseWare and YouTube
Teaching
- 18.226 Probabilistic Methods in Combinatorics (grad), Fall 2022
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18.A34 Mathematical Problem Solving (Putnam Seminar), Fall 2022
Putnam Competition results 2022, 2021, 2019, 2018, 2017
- 18.225 Graph Theory and Additive Combinatorics (grad), Fall 2021
- 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. - 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
Slides
- 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
Videos
- 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
Short CV
- 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