Associate Professor of Mathematics
Department of Mathematics
Massachusetts Institute of Technology

Email:

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

Former PhD Students: Benjamin Gunby, Jonathan Tidor, Aaron Berger, Ashwin Sah, Mehtaab Sawhney

(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

Teaching

• 18.225 Graph Theory and Additive Combinatorics (grad), Fall 2023 Book Exercises MIT OCW YouTube
• 18.A34 Mathematical Problem Solving (Putnam Seminar), Fall 2023 MIT News Profile
  Putnam Competition results 2023, 2022, 2021, 2019, 2018, 2017
  
• 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

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

• 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

Short CV

• Fulkerson Prize, 2024
• 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