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Number Theory Seminar

Ramanujan bigraphs

Brooke Feigon (City College NY)

Location:  Hill 525
Date & time: Tuesday, 10 December 2019 at 2:00PM - 3:00PM

Abstract:   In this talk I will describe a Cayley-style construction of biregular graphs (with two different degrees). I will give examples of this construction for both infinite families of Ramanujan and non-Ramanujan graphs. These examples are constructed from the unitary groups in three variables with the action of a simply transitive p-arithmetic lattice. The proof of the (non-)Ramanujan property follows from an analysis of the automorphic spectrum of U(3) via work of Rogawski, Shin and others.

This project is joint work with Cristina Ballantine, Shai Evra, Kathrin Maurischat and Ori Parzanchevski.