Department of Mathematics - Algebra and Geometry Seminar - Higher Segal spaces and algebraic structures

In this talk, I will introduce the 2-Segal conditions of Dyckerhoff and Kapranov, describing both the algebraic and geometric intuitions which lead to the 2-Segal conditions. I will then give an overview of how the algebraic intuition can be extended to classify various algebraic structures in (higher) categories of spans. I will additionally explain how the geometric intuition can be used to provide state-sum-style invariants of surfaces. Time permitting, I will then discuss work in progress on higher cyclic operads, inspired by intuitions which arise from the algebraic characterization of 2-Segal objects.