Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## A shrinking target problem in rank one homogeneous spaces

Talk by Dr. Cheng Zheng

**Date:** 16.05.22 **Time:** 14.05 - 15.05 **Room:** ETH HG G 43

The Khintchine’s theorem in the metric theory of Diophantine approximation says that the subset of Diophantine numbers of type r > 1 has full Lebesgue measure. The Jarník-Besicovitch theorem states further that its complement has Hausdorff dimension 2/(1 + r). A dynamical point of view on the Jarník-Besicovitch theorem is the shrinking target problem proposed by Hill and Velani. In this talk, we will discuss our work about a shrinking target problem in rank one homogeneous spaces and a result of Jarník-Besicovitch theorem in the metric theory of Diophantine approximation on Heisenberg groups. If time permits, we will also discuss the connection between our work and sparse equidistribution problem. Zoom link: https://ethz.zoom.us/j/65329488712