Speaker: Jinpeng An, Peking University Title: Homogeneous dynamics and Diophantine approximation Venue: B 924 Time:   14:00-16:00, May 29, 2012 Abstract: Homogeneous dynamics is a special kind of dynamical system where the space is a homogeneous manifold of a Lie group. Due to its close relationship to number theory, it has become an active area of research in recent years. We will discuss basic concepts and results in homogeneous dynamics with emphasis on the example SL(3,R)/SL(3,Z). We will also explain the relation of the example to Diophantine approximation, especially to the conjectures of Oppenheim, Littlewood, and Schmidt. References: [1] D. Badziahin, A. Pollington, S. Velani, On a problem in simultaneous Diophantine approximation: Schmidt's conjecture, Ann. of Math. (2) 174 (2011), no. 3, 1837--1883. [2] M. Einsiedler, A. Katok, E. Lindenstrauss, Invariant measures and the set of exceptions to Littlewood's conjecture, Ann. of Math. (2) 164 (2006), no. 2, 513--560. [3] G. Margulis, Oppenheim conjecture, in "Fields Medallists' lectures", 272--327, World Sci. Ser. 20th Century Math., 5, World Sci. Publ., River Edge, NJ, 1997.                                                   All ARE WELCOME!