Uploaded July 2026 | Updated September 2026, 3 days ago
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 5, Session 1
Speaker: Bharatram Rangarajan (Louvain)
Title: Zeta Functions for Finite Quotients of Affine Buildings
Abstract: In recent years, there has been interest in generalizing the zeta identity from graphs to higher dimensional simplicial complexes, motivated in part by its significance in the definition and study of \Ramanujan complexes and high-dimensional expanders. In a line of work by Li-Kang, such a zeta function is defined in dimension 2 (namely for buildings associated to PGL(3)). In joint ongoing work with Ori Parzanchevski, we reprove the Kang-Li zeta identity above using a "local" approach, where we explicitly describe the relations between eigenvectors of the collision-free (or non-backtracking) operators in different dimensions, significantly building on the basic idea used by Lubetsky-Peres in the case of graphs.
The 25th Midrasha Mathematicae on Groups, Expanders and Codes -- Celebrating Alex Lubotzky's 70th birthday.
Day 5, Session 1
Speaker: Bharatram Rangarajan (Louvain)
Title: Zeta Functions for Finite Quotients of Affine Buildings
Abstract: In recent years, there has been interest in generalizing the zeta identity from graphs to higher dimensional simplicial complexes, motivated in part by its significance in the definition and study of \Ramanujan complexes and high-dimensional expanders. In a line of work by Li-Kang, such a zeta function is defined in dimension 2 (namely for buildings associated to PGL(3)). In joint ongoing work with Ori Parzanchevski, we reprove the Kang-Li zeta identity above using a "local" approach, where we explicitly describe the relations between eigenvectors of the collision-free (or non-backtracking) operators in different dimensions, significantly building on the basic idea used by Lubetsky-Peres in the case of graphs.
