- Equiangular lines with a fixed angle (with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang) blog
Directed graphs and tournaments
- Triforce and corners (with Jacob Fox, Ashwin Sah, Mehtaab Sawhney, and David Stoner)
Mathematical Proceedings of the Cambridge Philosophical Society, to appear.
- On the number of Hadamard matrices via anti-concentration (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 28 (2019), 777–790.
Efficient arithmetic regularity and removal lemmas for induced bipartite patterns (with Noga Alon and Jacob Fox) slides
Discrete Analysis 2019:3, 14 pp.
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)
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.
Independent sets and graph homomorphisms
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)
Journal of Combinatorial Theory Series B 138 (2019), 172–195. blog MIT News
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 372 (2019), 3019–3062.
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.
Energy-minimizing error-correcting codes (with Henry Cohn)
IEEE Transactions on Information Theory 60 (2014), 7442–7450.
Exponential improvements for superball packing upper bounds (with Ashwin Sah, Mehtaab Sawhney, and David Stoner)
Extremal and Ramsey graph theory
The critical window for the classical Ramsey-Turán problem (with Jacob Fox and Po-Shen Loh)
Combinatorica 35 (2015), 435–476.
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.
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 Green-Tao 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
Young tableaux and the representations of the symmetric group
Harvard College Mathematics Review 2 (2008), 33–45.