Class of 1956 Career Development Assistant Professor
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 areas
Combinatorics, discrete mathematics, graph theory
Coorganizer of MIT Combinatorics Seminar
Current PhD students: Aaron Berger, Benjamin Gunby, Mehtaab Sawhney, Jonathan Tidor
Teaching
 18.226 Probabilistic Methods in Combinatorics (grad), Fall 2020
 18.A34 Mathematical Problem Solving (Putnam Seminar), Fall 2020
 18.217 Graph Theory and Additive Combinatorics (grad), Fall 2019
Lecture videos on MIT OCW and YouTube  18.211 Combinatorial Analysis, Fall 2018
 Polynomial Method in Combinatorics (grad), Trinity Term 2016, Oxford
Book project: Graph Theory and Additive Combinatorics
Math Olympiad training handouts
Selected publications

Joints of varieties (with Jonathan Tidor and HungHsun Hans Yu)

Equiangular lines with a fixed angle (with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang)

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. 
An $L^p$ theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions (with Christian Borgs, Jennifer T. Chayes, and Henry Cohn)
Transactions of the American Mathematical Society 372 (2019), 3019–3062. 
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
 The joints problem for varieties
 Equiangular lines, spherical twodistance sets, and spectral graph theory
 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
 The joints problem for varieties, Big Seminar by Laboratory of Combinatorial and Geometric Structures, Aug 2020
 Equiangular lines, spherical twodistance sets, and spectral graph theory, DIMAP, Dec 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
 Large deviations for arithmetic progressions, Simons Institute, Berkeley, Apr 2017
 Sparse graph regularity tutorial, Simons Institute, Berkeley, Jan 2017
 Green–Tao theorem and a relative Szemerédi theorem, Simons Institute, Berkeley, Dec 2013
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