Discrete Transitive Actions on the Vertices of Bruhat-Tits Buildings

NUMBER THEORY
Topic:Discrete Transitive Actions on the Vertices of Bruhat-Tits Buildings
Speaker:Alireza Salehi Golsefidy
Affiliation:Princeton University, Member, School of Mathematics
Date:Thursday, October 26
Time/Room:4:30pm - 5:30pm/Princeton University, Fine Hall 214

In this work, joint with A. Mohammadi, we try to classify all the discrete transitive actions on the vertices of a Bruhat-Tits Building over a local field of characteristic zero. There are lots of such actions in the case of Bruhat-Tits tree, i.e. rank one case. However these actions are rare in the higher rank; in fact, only a few are known in dimension at most five. In this talk, I will explain a recent theorem stating that there are no such actions in dimension larger than 8. In the proof we will work with the arithmetic structure of such actions and make use of Tamagawa numbers and Prasad's work.