Falconer's distance set conjecture and its many faces
Dr. Ruixiang Zhang
2024-01-08 16:00-17:00
MCM110&ZOOM
Speaker: Dr. Ruixiang Zhang (UC Berkeley) Time: 16:00-17:00 January 8, 2024 (Monday)
Place: MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Falconer's distance set conjecture and its many faces
Abstract: In 1985, Falconer made the conjecture that whenever $E \subset \mathbb{R}^2$ has dimension $>1$, its distance set $\Delta(E) = \{|x-y|: x, y \in E\}$ will have positive measure. Despite its innocent appearance, this conjecture remains unsolved as of today. We will introduce this conjecture and three interesting results towards it. The methods to prove these results are related to Fourier analysis, classical algebraic geometry/topology and geometric measure theory.
