Yewen Sun
The Ohio State University
Title
A symmetric multivariate Elekes-Rónyai theorem
Abstract
The Elekes-Rónyai theorem is a well-known result in additive combinatorics. Their work has been significantly generalized and improved by many mathematicians, in part due to its connections to other areas such as geometry and model theory. In 2020, Ray and Tov extended the Elekes-Rónyai theorem to higher dimensions. Jing, Roy, and Tran later proved a symmetric version of the theorem in 2022. In this talk, we will discuss our recent work generalizing the symmetric Elekes-Rónyai theorem to higher dimensions. We also proved an Erdős-Szemerédi-type theorem for two polynomials in higher dimensions, generalizing a result by Jing, Roy, and Tran. The key ingredient in our proofs is a variation of a theorem by Elekes, Nathanson, and Ruzsa.
