Speaker: Julie Bergner (Virgina)
Title: Combinatorial examples of 2-Segal sets and their Hall algebras
Abstract: The notion of a 2-Segal set encodes an algebraic structure that is similar to that of a category, but for which composition need not exist or be unique, yet is still associative. The fact that such structures give rise to Hall algebras, generalizing constructions in representation theory and algebraic geometry, is one of the primary motivations for studying them. In this talk, we look at 2-Segal sets that arise from trees and graphs and their associated Hall algebras. These examples are discrete versions of the analogous 2-Segal spaces of trees and graphs developed by Gálvez-Carrillo, Kock, and Tonks, and provide a way to explore various general constructions quite explicitly. Much of this work is joint with Borghi, Dey, Gálvez-Carrillo, and Hoekstra Mendoza.