Combinatorics Seminar - Yufei Zhao
16:00-18:00
Speaker: Yufei Zhao
Title: The geometry of transitive sets, with applications to eigenbasis of Cayley graphs
Abstract: I will discuss some counterintuitive facts and conjectures about the width of a finite transitive subset of a high dimensional sphere (here "transitive" means transitive under the orthogonal group). We were motivated by the question of whether Cayley graphs always have a bounded eigenbasis. I will explain this connection, and mention several open problems.
Based on joint work with Ashwin Sah and Mehtaab Sawhney: https://arxiv.org/abs/2005.04502 and https://arxiv.org/abs/2101.11207