Research
 Research papers  Expositions and surveys 
My papers are also listed on arXiv, MathSciNet, and Google Scholar.
Research Papers
Random matrices
 On the number of Hadamard matrices via anticoncentration (with Asaf Ferber and Vishesh Jain)
Regularity lemmas and applications

On regularity lemmas and their algorithmic applications (with Jacob Fox and László Miklós Lovász)
Combinatorics, Probability and Computing, 26 (2017), 481–505. 
A fast new algorithm for weak graph regularity (with Jacob Fox and László Miklós Lovász)
Combinatorics, Probability and Computing, to appear. 
Efficient arithmetic regularity and removal lemmas for induced bipartite patterns (with Noga Alon and Jacob Fox) slides
Cayley graphs

Quasirandom Cayley graphs (with David Conlon)
Discrete Analysis 2017:6, 14 pp. 
Hypergraph expanders of all uniformities from Cayley graphs (with David Conlon and Jonathan Tidor)
The GreenTao theorem and a relative Szemerédi theorem slides video

A relative Szemerédi theorem (with David Conlon and Jacob Fox)
Geometric and Functional Analysis 25 (2015), 733–762.
Companion note: Linear forms from the Gowers uniformity norm 
An arithmetic transference proof of a relative Szemerédi theorem
Mathematical Proceedings of the Cambridge Philosophical Society 156 (2014), 255–261. 
A short proof of the multidimensional Szemerédi theorem in the primes (with Jacob Fox)
American Journal of Mathematics 137 (2015), 1139–1145.
Large deviations in random graphs slides

On replica symmetry of large deviations in random graphs (with Eyal Lubetzky)
Random Structures & Algorithms 47 (2015), 109–146. blog 
On the variational problem for upper tails in sparse random graphs (with Eyal Lubetzky)
Random Structures & Algorithms 50 (2017), 420–436. blog 
On the lower tail variational problem for random graphs
Combinatorics, Probability and Computing 26 (2017), 301–320. 
Upper tails and independence polynomials in random graphs (with Bhaswar B. Bhattacharya, Shirshendu Ganguly, and Eyal Lubetzky)
Advances in Mathematics 319 (2017), 313–347. 
Upper tails for arithmetic progressions in a random set (with Bhaswar B. Bhattacharya, Shirshendu Ganguly, and Xuancheng Shao) video
International Mathematics Research Notices. IMRN, to appear.
Graph limits

Hypergraph limits: a regularity approach
Random Structures & Algorithms 47 (2015), 205–226. 
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, to appear. 
An $L^p$ theory of sparse graph convergence II: LD convergence, quotients, and right convergence (with Christian Borgs, Jennifer T. Chayes, and Henry Cohn)
Annals of Probability 46 (2018), 337–396. 
On derivatives of graphon parameters (with László Miklós Lovász)
Journal of Combinatorial Theory, Series A 145 (2017), 364–368.
Sphere packing and energy minimization

Sphere packing bounds via spherical codes (with Henry Cohn)
Duke Mathematical Journal 163 (2014), 1965–2002. 
Energyminimizing errorcorrecting codes (with Henry Cohn)
IEEE Transactions on Information Theory 60 (2014), 7442–7450.
Extremal and Ramsey graph theory

Extremal results in sparse pseudorandom graphs (with David Conlon and Jacob Fox)
Advances in Mathematics 256 (2014), 206–290. slides 
The critical window for the classical RamseyTurán problem (with Jacob Fox and PoShen Loh)
Combinatorica 35 (2015), 435–476.
Independent sets and graph homomorphisms

The number of independent sets in a regular graph
Combinatorics, Probability and Computing 19 (2010), 315–320. poster 
The number of independent sets in a graph with small maximum degree (with David Galvin)
Graphs and Combinatorics 27 (2011), 177–186. 
The bipartite swapping trick on graph homomorphisms
SIAM Journal on Discrete Mathematics 25 (2011), 660–680. poster 
The number of independent sets in an irregular graph (with Ashwin Sah, Mehtaab Sawhney, and David Stoner) blog

A reverse Sidorenko inequality (with Ashwin Sah, Mehtaab Sawhney, and David Stoner) slides blog
More sums than differences sets slides

Constructing MSTD sets using bidirectional ballot sequences
Journal of Number Theory 130 (2010), 1212–1220. extended version 
Counting MSTD sets in finite Abelian groups
Journal of Number Theory 130 (2010), 2308–2322. 
Sets characterized by missing sums and differences
Journal of Number Theory 131 (2011), 2107–2134.
Other topics

Constructing numerical semigroups of a given genus
Semigroup Forum 80 (2010), 242–254. 
The coefficients of a truncated Fibonacci power series
Fibonacci Quarterly 46/47 (2009), 53–55.
Expositions and surveys

The GreenTao theorem: an exposition (with David Conlon and Jacob Fox)
EMS Surveys in Mathematical Sciences 1 (2014), 249–282. 
Extremal regular graphs: independent sets and graph homomorphisms
American Mathematical Monthly 124 (2017), 827–843. blog
Older expository papers and notes

Biased riffle shuffles, quasisymmetric functions, and the RSK algorithm

Young tableaux and the representations of the symmetric group
Harvard College Mathematics Review 2 (2008), 33–45.