Papers and preprints

• (with Rachel Greenfeld and Marina Iliopoulou) On integer distance sets. arXiv 2401.10821.


• (with Ashwin Sah and Mehtaab Sawhney) Effective bounds for Roth's theorem with shifted square common difference. arXiv 2309.08359.


• (with K. Soundararajan) Divisibility of character values of the symmetric group by prime powers. arXiv 2301.02203.


• (with Ben Krause, Mariusz Mirek, and Jim Wright) Polynomial progressions in topological fields. arXiv 2210.00670.


• Subsets of F_p^n x F_p^n without L-shaped configurations. Compos. Math., 160(1), 176-236, 2024.


• (with K. Soundararajan) Almost all entries in the character table of the symmetric group are multiples of any given prime. J. Reine Angew. Math. 786:45-53, 2022.


• On even entries in the character table of the symmetric group. arXiv 2007.06652.


• An asymptotic version of the prime power conjecture for perfect difference sets. Math. Ann. 380 (2021), no. 3-4, 1387-1425.


• (with Sean Prendiville) A polylogarithmic bound in the non-linear Roth Theorem. Int. Math. Res. Not. (2022), no. 8, 5658-5684.


• Bounds for sets with no polynomial progressions. Forum Math. Pi 8 (2020), e16.


• (with Sean Prendiville) Quantitative bounds in the non-linear Roth Theorem. arXiv 1903.02592.


• On the polynomial Szemer\'edi theorem in finite fields. Duke Math. J. 168 (2019), no. 5, 749-774.


• Three-term polynomial progressions in subsets of finite fields. Israel J. Math. 228 (2018), no. 1, 379-405.


• Mixing for three-term progressions in finite simple groups. Math. Proc. Cambridge Philos. Soc. 165(2):279-286, 2018.

Expository

• Finite field models in arithmetic combinatorics--twenty years on. The survey accompanying my talk at the 2024 British Combinatorial Conference


• Recent progress on bounds for sets with no three terms in arithmetic progression [after Bloom and Sisask, Croot, Lev, and Pach, and Ellenberg and Gijswijt]. Astérisque (2022), no. 438, exp. no. 1196, 547-581, Séminaire Bourbaki. vol. 2021/2022. exposés 1181-1196.

Additive Combinatorics 2024

High-dimensional phenomena in discrete analysis

GLNT Seminar

MAGNTS

IAS Women and Mathematics

IAS Special Year Research Seminar

Analysis and TCS: New Frontiers

Joint IAS/Princeton Number Theory Seminar

Webinar in Additive Combinatorics