James Leng

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20232025

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math.CO2024

Improved Bounds for Szemerédi's Theorem

James Leng, Ashwin Sah, Mehtaab Sawhney

Let $r_{k} (N)$ denote the size of the largest subset of $[N] = {1, \dots, N}$ with no $k$ -term arithmetic progression. We show that for $k \geq 5$ , there exists $c_{k} > 0$ such that \[r_…

math.CO2024

Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm

James Leng, Ashwin Sah, Mehtaab Sawhney

We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input rece…

Improved Bounds for Szemerédi's Theorem

Quasipolynomial bounds on the inverse theorem for the Gowers Us+1[N]-norm

Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm