- Quasirandom Cayley graphs (with David Conlon)
Discrete Analysis 2017:6, 14 pp.
- Group representations that resist worst-case sampling
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
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)
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, to appear.
On derivatives of graphon parameters (with László Miklós Lovász)
Journal of Combinatorial Theory, Series A 145 (2017), 364–368.
Graph regularity lemma and applications
- On regularity lemmas and their algorithmic applications
(with Jacob Fox and László Miklós Lovász)
Combinatorics, Probability and Computing, 26 (2017), 481–505.
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.
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.
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
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, to appear. blog
Older expository papers and notes
Young tableaux and the representations of the symmetric group
Harvard College Mathematics Review 2 (2008), 33–45.