SSE Talk | 下周讲座预告

Dear all,

You are cordially invited to an academic seminar. Please find the details as follows.

Seminar Information

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Topic: Edge Zeta Functions of Spherical Buildings: A Journey through Combinatorics and Representation Theory

Time & Date: 5:00-6:00 PM, December 4 (Monday)

Venue: Room 106, Teaching A

Speaker: Dr. Jianhao SHEN, The Chinese University of Hong Kong

Host: Prof. Caihua LUO, The Chinese University of Hong Kong, Shenzhen

Abstract: 

The zeta function of a graph captures essential connectivity properties and has found diverse applications. We generalize this concept by defining edge zeta functions for spherical buildings associated with finite general linear groups. To analyze these zeta functions, we undertake a journey through combinatorics and representation theory. By introducing and applying insightful tools including digraphs X_0 and X_2, cyclic n-partite graphs, partite-transitive group actions, and Springer's theorem on Hecke algebras, we derive elegant formulas for the zeta functions of buildings of general linear groups. The eigenvalues are revealed to be roots of unity times powers of q. This demonstrates the power of combining algebraic, graph-theoretic and representation-theoretic perspectives when exploring rich mathematical structures like buildings.

Bios:

Dr. Jianhao SHEN is a Ph.D. student of Prof. Jiu-Kang YU at The Chinese University of Hong Kong. His thesis is about zeta functions of spherical buildings.

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