researchseminars.org

Xu Gao (UC Santa Cruz)
2023-03-16 21:00 - 22:00 UTC | https://researchseminars.org/talk/UCSD_NTS/83/
Title: $p$-adic representations and simplicial distance in Bruhat-Tits buildings (https://researchseminars.org/talk/UCSD_NTS/83/)
by Xu Gao (UC Santa Cruz) as part of UCSD number theory seminar

Lecture held in APM 6402 and online.

Abstract
$p$-adic representations are important objects in number theory, and stable lattices serve as a connection between the study of ordinary and modular representations. These stable lattices can be understood as stable vertices in Bruhat-Tits buildings. From this viewpoint, the study of fixed point sets in these buildings can aid research on $p$-adic representations. The simplicial distance holds an important role as it connects the combinatorics of lattices and the geometry of root systems. In particularly, the fixed-point sets of Moy-Prasad subgroups are precisely the simplicial balls. In this talk, I'll explain those findings and compute their simplicial volume under certain conditions.

pre-talk at 1:20pm
