Time：14:00-15:00, Tuesday, April 15 2025
Venue：E4-233
Host: Zipeng Wang, ITS
Speaker: Omri Sarig, The Weizmann Institute of Science
Biography: Professor Sarig received his Ph. D. from Tel-Aviv University in 2001. He made certain important contributions to ergodic theory and dynamical systems and was an invited speaker at International Congress of Mathematicians 2010. He won a number of distinguished awards including Michael Brin Prize in Dynamical Systems and Erdös Prize 2013. His research bridges deterministic models with probabilistic behavior, impacting mathematics and physics.
Title：Irregularities in Uniform Distribution
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 be have 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.
