Workshop on Representation Theory and Analysis on Locally Symmetric Spaces | |

Topic: | Thin part of arithmetic locally symmetric spaces |

Speaker: | Mikolaj Fraczyk |

Affiliation: | Renyi Institute |

Date: | Wednesday, March 7 |

Time/Room: | 10:00am - 11:00am/Simonyi Hall 101 |

Abstract: Let $R>0$. The R-thin part of a locally symmetric space is defined as the set of points where the R-ball is not isometric to an R-ball in the universal cover. Recently Abert et al. showed that if X is a higher rank symmetric space whose isometry group has Kazhdan's property (T), then the volume of the R-thin part of finite volume quotients M of X is asymptotically $o(Vol(M))$. It is conjectured that the same holds true for congruence arithmetic quotients of rank-1 symmetric spaces. In this talk I will present a solution (joint work with Jean Raimbault) of this conjecture for congruence arithmetic hyperbolic orbifolds of dimension 2 and 3. I will discuss some applications to topology and the relation of this problem to the limit multiplicity property for sequences of arithmetic congruence lattices.