Title: Approximate groups
Speaker: Yifan Jing
Abstract: Approximate group is a central concept in arithmetic combinatorics, with deep connections to number theory, geometry, group theory, and harmonic analysis. In this talk, we will introduce the notion of approximate groups, highlighting their importance as a natural generalization of exact groups. We will explore key examples and discuss foundational results such as Freiman’s theorem, which connects approximate groups to structural classification problems. Additionally, we will touch on applications of approximate groups in tackling problems related to sum-product phenomena, the behavior of polynomials, and progress in higher order Fourier analysis. By the end of the talk, participants will have a better understanding of how approximate groups serve as a bridge between algebraic and analytic perspectives in modern mathematical research.
