### Mathematics Colloquium

# Seonhee Lim

### (Seoul National University)

## "Dynamics on Homogeneous Spaces and Number Theory"

** Date: ** |
Fri, February 3, 2017 |

** Time: ** |
14:15 |

** Place: ** |
Lecture Hall, Research II |

**Abstract:** We will go over some geometric properties of homogeneous spaces and dynamical properties of Lie group actions on homogeneous spaces, especially diagonal and unipotent actions on \(\mathrm{SL}_n(\mathbb{R})/\mathrm{SL}_n(\mathbb{Z})\). We will explain how these properties can be used to prove certain problems in Diophantine approximation. Especially two questions, one on Oppenheim conjecture and the other on badly approximable sets, will be discussed.

*The colloquium is preceded by tea from 13:45 in the Resnikoff Mathematics Common Room, Research I, 127.*