$p$-adic representations and simplicial distance in Bruhat-Tits buildings

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.

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:20pm

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.