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, additive, graph theory, discrete geometry)

MIT-Harvard-MSR Combinatorics Seminar, co-organizer

**Current PhD students**:
Aaron Berger,
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 OCW and YouTube

## Teaching

- 18.226 Probabilistic Methods in Combinatorics (grad), Fall 2022
- 18.A34 Mathematical Problem Solving (Putnam Seminar), Fall 2022

*Putnam Competition**2021 results**2019 results* - 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)
- 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