Irregularities in Uniform Distribution
报告人：Omri Sarig (The Weizmann Institute of Science)
时间：2025-07-23 15:30-16:30
地点： Room 313, Zhihua Building
Abstract: Suppose a is an irrational number. Weyl proved that na mod 1 is uniformly distributed on the unit interval. i.e., the frequency of visits of na mod 1 to a subinterval of [0,1] tends to the length of the subinterval. It has long been known that the error term in this limit theorem can exhibit strong bias, reflecting an “irregularity” in uniform distribution in the higher-order term. This bias depends on the fine number theoretic properties of a. For example, the square roots of two and three do not behave the same way (!) I will explain how infinite ergodic theory can shed light on this phenomenon, and describe some recent joint work with Dmitry Dolgopyat on the equidistribution of the error term. There are amusing connections to the geometry of translation surfaces with infinite genus, and to local limit theorems of inhomogeneous Markov chains.
Biography: Professor Omri Sarig is a leading mathematician in ergodic theory and dynamical systems. His work bridges deterministic models with probabilistic behavior. He was an ICM 2010 invited speaker, and received the Michael Brin Prize and Erdős Prize (2013) for his groundbreaking research.
