Title: Nondense orbits of homogeneous dynamics

Speaker: Jinpeng An, Peking University

Time/Venue: 14:00-15:00, 13 NOV., B1044

Abstract: Homogeneous dynamics is a special kind of dynamical systems given by Lie groups. For certain important cases, the systems are ergodic and hence the points with nondense orbits form a set of measure zero. However, the behavior of nondense orbits reflects the complexity of the system and is related to problems in number theory. In this talk, we will discuss some recent progresses of investigations in nondense orbits of homogeneous dynamics, with emphasis on properties of bounded orbits. We will also explain their relations with problems in number-theoretic problems.

Title: Bounded orbits and winning sets

Speaker: Jinpeng An, Peking University

Time/Venue: 14:00-15:00, 15 NOV., B1044

Abstract: We will explain the notion of a winning set for Schmidt's game and its variants, and sketch the proofs of some results concerning bounded orbits of homogeneous dynamics mentioned in the previous talk.