Fractal Uncertainty Principle and Applications
Time: 2021-12-31
Published By: Wenqiong Li
Speaker(s): Long Jin(Tsinghua University)
Time: 16:00-17:00 January 4, 2022
Venue: Room 77201, Jingchunyuan 78, BICMR
Abstract: In this talk, we survey some recent progress on the fractal uncertainty principle and its applications. Roughly speaking, a fractal uncertainty principle states that a function and its Fourier transform cannot be both localized near a fractal set. This is first formulated by Dyatlov--Zahl in 2016 to understand the essential spectral gap for convex cocompact hyperbolic manifolds and fully resolved by Bourgain--Dyatlov in one-dimensional situation in 2018. We will discuss the current understanding on this topic as well as its further applications in the field of quantum chaos.
