Peter Haine, UC Berkeley

Title: Exit-path categories in topology and algebraic geometry

Abstract: Given a (nice) connected topological space T, local systems on T can be understood as representations of the fundamental group of T. Similarly, given a connected scheme X, étale local systems on X can be understood as representations of the étale fundamental group of X. This suggests a general phenomenon: in many situations, a category of sheaves should be expressible in terms of representations of a more simple/combinatorial object. This more combinatorial object is called an “exit-path category”. In this talk, we’ll explore these invariants in both topology and algebraic geometry. Exit-path categories have applications in a variety of areas, including mirror symmetry, Stokes data, K-theory, étale homotopy theory, and anabeliain geometry; we’ll highlight some of these applications as well. This will cover joint work with a number of collaborators, including Barwick, Glasman, Porta, and Teyssier.TBA