Nondense orbits for homogeneous dynamics and nondense geodesics in locally symmetric spaces
Prof. Jinpeng An
2023-05-18 15:30-16:30
MCM110
Speaker: Prof. Jinpeng An (Peking University)Time: 15:30-16:30 May 18, 2023 (Thursday)
Place: MCM110
Title: Nondense orbits for homogeneous dynamics and nondense geodesics in locally symmetric spaces
Abstract: Homogeneous dynamics is a special kind of dynamics given by Lie groups, and is closely related to problems in geometry and number theory. In this talk, we are interested in orbits of such dynamics that are not dense in the phase space, with special attention on those orbits whose closures do not intersect a given set. Under certain conditions, the points with the latter kind of orbits can be proved to form a set of full Hausdorff dimension. As a geometric application, one can prove that there are plenty of geodesics in a locally symmetric space of noncompact type whose closures do not intersect any given countable subset. This is a joint work with Lifan Guan and Dmitry Kleinbock.
