Corners with Polynomial Side Length - Noah Kravitz

Joint IAS/PU Groups and Dynamics Seminar
4:30pm|Simonyi 101
Topic: Corners with Polynomial Side Length
Speaker: Noah Kravitz
Affiliation: Princeton University
Date: December 10, 2024
We prove ''reasonable'' quantitative bounds for sets in ℤ2
avoiding the polynomial corner configuration (x,y),(x+P(z),y),(x,y+P(z)), where P is any fixed integer-coefficient polynomial with an integer root of multiplicity 1. This simultaneously generalizes a result of Shkredov about corner-free sets and a recent result of Peluse, Sah, and Sawhney about sets without 3-term arithmetic progressions of common difference z2−1. Two ingredients in our proof are a general quantitative concatenation result for multidimensional polynomial progressions and a new degree-lowering argument for box norms. Joint work with Borys Kuca and James Leng.