Zuxiang Kong
The Ohio State University
Title
Projections, fiber spillover and the Ruzsa’s conjecture
Abstract
Given a subset of a group, it is natural to ask how the doubling constant behaves under a group homomorphism, or equivalently under taking a quotient projection. This was answered in 2024 in joint work with Fei Peng and Chieu Minh Tran, which I will discuss in the first part of the talk and introduce previously established bounds for the doubling constants of projections in locally compact unimodular groups, as well as a structural result. One of the key tools used was what we call the Spillover technique, a geometric idea that tracks fiber-level interactions under doubling. As it turns out, this viewpoint remains robust and has led to the recent resolution of the Ruzsa’s conjecture, a central problem in Additive Combinatorics that has been open since 1999, which concerns the size of the subgroup generated by a set in a finite abelian group with bounded exponent. In joint work with Yifan Jing and Souktik Roy, we establish the conjectured exponential dependence with an optimal leading coefficient in the exponent. If time permits, I will also discuss an extension to 2-steps nilpotent groups.
