Associate Professor of Mathematics
Department of Mathematics
Massachusetts Institute of Technology
Email:
Office: 2271
Mail:
MIT Department of Mathematics
77 Massachusetts Ave, Bldg 2271
Cambridge, MA 02139, USA
Research Interests: Combinatorics
 extremal, probabilistic, and additive combinatorics
 graph theory; discrete geometry; applications to computer science
Coorganizer, MITHarvardMSR Combinatorics Seminar
Associate Editor, Advances in Mathematics
Editorial Advisory Board Member, Springer Graduate Texts in Mathematics
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
(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

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 HungHsun Hans Yu)
Geometric and Functional Analysis 32 (2022) 302–339  Testing linearinvariant 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 GreenTao 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