### Towards a zero-one law for improvements to Dirichlet's approximation theorem

Abstract

In this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was introduced by Kleinbock and Wadleigh in 2018 and generalizes the classical notion of a matrix being Dirichlet-improvable. In particular, we prove a partial zero-one law for the Lebesgue measure of the set of $\psi$-Dirichlet matrices. Joint with Dmitry Kleinbock and Andreas Strömbergsson.

（1）丢番图逼近

（2）齐性动力系统

• ### Some ergodic optimization problems for expanding circle maps

AbstractIn this talk, we consider some ergodic optimization problems for an expanding circle map. When the map is real analytic, we show that all optimizing measures of a real analytic potential function have zero entropy, unless the potential is cohomologous to constant. We also discuss some applications and related problems. This talk is based on a joint work with Weixiao Shen.Speaker高睿，研...

• ### Mixing time for the asymmetric simple exclusion process in a random environment

peaker杨尚杰Bar-Ilan UniversityI am a postdoctoral fellow hosted by Prof. Gidi Amir in the mathematics department of Bar-Ilan University .Before that, I was a postdoc hosted by Prof. Tertuliano Franco in UFBA, and a Ph.D student under the supervision of Prof. Hubert Lacoin at IMPA. Here are my CV and thesis: Mixing time for interface models and particle system . I am mainly interested in probab...