$p$-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 -adic representations. The simplicial balls, in particular, hold an important role as they possess the most symmetry and fastest growth, and are closely related to the Moy-Prasad filtrations. In this talk, I will introduce some results on simplicial balls.
$p$-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 $-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.
$p$-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 $-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.
$p$-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 $-adic representations. The simplicial balls, in particular, hold an important role as they possess the most symmetry and fastest growth, and are closely related to the Moy-Prasad filtrations. In this talk, I'll explain those new findings, provide a characterization of such simplicial balls, and compute their simplicial volume under certain conditions.
How many vertices are there in a simplicial ball of radius r (in a Brihat-Tits Building)?
UCSC Graduate Colloquium, May 9, 2022. (Slides)
Stable Simplexes of p-adic Representations in Bruhat-Tits Buildings.
UCSC Graduate Colloquium, November 22, 2021. (Slides)
Sparsity of Algebraic Points, MSRI Summer Graduate School
Mathematical Sciences Research Institute, June 7–18, 2021
Topology and Arithmetic, Arizona Winter School
University of Arizona, March 2–6, 2019
Vertex Operator Algebras and Related Topics
Sichuan University, August, 2019
Workshop on Lie Theory and Representation Theory
Sichuan University, May, 2016
The Lie Theory Workshop
Sichuan University, July, 2014
Sino-French Conference on Arithmetic Geometry
Nankai University, June, 2013
Arakelov geometry
with Jianqi Liu and Yufei Zhang
Fall 2019 – Spring 2020
Homotopical algebras
with Tzu-Mo Kuo, Jianqi Liu, Yufei Shan and Yufei Zhang
Winter 2019 – Fall 2019
Homological algebras
with Tzu-Mo Kuo, Jianqi Liu, Yufei Shan and Yufei Zhang
Fall 2018
D-modules
with Tzu-Mo Kuo and Yufei Shan
Fall 2017 – Fall 2018
Chiral algebras
with Yiyi Zhu
Spring & Summer 2017
Primes in arithmetic progressions
with Hanbin Zhang
Spring 2016
Algebraic geometry
with Hanbin Zhang
Fall 2015 – Spring 2016
Neukirch’s algebraic number theory
with Hanbin Zhang and Yiyi Zhu
Fall 2014 – Spring 2015
Category theory
with Hanbin Zhang and Yiyi Zhu
Fall 2013 – Spring 2014