The Green-Tao theorem and a relative Szemerédi theorem
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.
Graph regularity method and applications
Extremal results in sparse pseudorandom graphs (with David Conlon and Jacob Fox)
Advances in Mathematics 256 (2014), 206–290.
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.
The regularity method for graphs with few 4-cycles (with David Conlon, Jacob Fox, and Benny Sudakov)
Triforce and corners (with Jacob Fox, Ashwin Sah, Mehtaab Sawhney, and David Stoner)
Mathematical Proceedings of the Cambridge Philosophical Society, 169 (2020), 209–223.
Common and Sidorenko linear equations (with Jacob Fox and Huy Tuan Pham)
The Quarterly Journal of Mathematics, to appear.
Patterns without a popular difference (with Ashwin Sah and Mehtaab Sawhney)
Tower-type bounds for Roth’s theorem with popular differences (with Jacob Fox and Huy Tuan Pham)
A short proof of the canonical polynomial van der Waerden theorem (with Jacob Fox and Yuval Wigderson)
Comptes Rendus Mathématique, to appear.
Arithmetic regularity and applications
Efficient arithmetic regularity and removal lemmas for induced bipartite patterns (with Noga Alon and Jacob Fox)
Discrete Analysis 2019:3, 14 pp.
Induced arithmetic removal: complexity 1 patterns over finite fields (with Jacob Fox and Jonathan Tidor)
Testing linear-invariant properties (with Jonathan Tidor)
FOCS 2020, accepted.
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)
Proceedings of the London Mathematical Society 121 (2020), 1311–1336.
Cayley graphs without a bounded eigenbasis (with Ashwin Sah and Mehtaab Sawhney)
International Mathematics Research Notices. IMRN, to appear.
Equiangular lines and spectral graph theory
Equiangular lines with a fixed angle (with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang)
Spherical two-distance sets and eigenvalues of signed graphs (with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang)
Joints tightened (with Hung-Hsun Hans Yu)
Joints of varieties (with Jonathan Tidor and Hung-Hsun Hans Yu)
Nonnegative rank and extension complexity
- Extension complexity of low-dimensional polytopes (with Matthew Kwan and Lisa Sauermann)
Independent sets and graph homomorphisms
The number of independent sets in a regular graph
Combinatorics, Probability and Computing 19 (2010), 315–320.
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.
- 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.
- A reverse Sidorenko inequality (with Ashwin Sah, Mehtaab Sawhney, and David Stoner)
Inventiones Mathematicae 221 (2020), 665–711.
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)
Advances in Mathematics, 365 (2020), 107056
Large deviations in random graphs
On replica symmetry of large deviations in random graphs (with Eyal Lubetzky)
Random Structures & Algorithms 47 (2015), 109–146.
On the variational problem for upper tails in sparse random graphs (with Eyal Lubetzky)
Random Structures & Algorithms 50 (2017), 420–436.
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)
International Mathematics Research Notices. IMRN 2020, 167–213.
On the upper tail problem for random hypergraphs (with Yang Liu)
Random Structures & Algorithms, to appear.
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.
A counterexample to the Bollobás-Riordan conjectures on sparse graph limits (with Ashwin Sah, Mehtaab Sawhney, and Jonathan Tidor)
- On the number of Hadamard matrices via anti-concentration (with Asaf Ferber and Vishesh Jain)
Directed graphs and tournaments
- Impartial digraphs (with Yunkun Zhou)
Combinatorica, to appear.
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
Constructing MSTD sets using bidirectional ballot sequences
Journal of Number Theory 130 (2010), 1212–1220.
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.
Older expository papers and notes
Young tableaux and the representations of the symmetric group
Harvard College Mathematics Review 2 (2008), 33–45.