Nondense orbits of homogeneous dynamics
Student No.:80
Time:Fri 16:30-17:30, Oct.26
Instructor:安金鹏 An Jinpeng  
Place:Lecture hall, Jin Chun Yuan West Bldg.
Starting Date:2018-10-26
Ending Date:2018-10-26

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 certain important number-theoretic problems. 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 theory.

About speaker:
Professor Jinpeng An now works at the Institute of Mathematical Sciences of Peking University. His research focuses on the lie theory and dynamics of group Actions. Great progress has been made in the function of subgroups in homogeneous space and the approximation problem of diophantine graphs. In particular, it has been proved that the two-dimensional weighted inferior approximation vector set is the resultant set. Therefore, a new proof of Schmidt's conjecture is given and stronger results are obtained. In cooperation with other scholars, they proved some properties of subgroup dimension data, solved two lie group problems proposed by famous mathematician Langlands, applied the results to spectral geometry, and proved single connected compact Riemannian manifolds with equal spectrum but different embryos.