Sam McCrosson (Dept. of Mathematical Sciences, MSU) 

03/10/2022  2:00pm

Abstract:  A classic type of result in math is showing two apparently dissimilar structures are actually the same. A striking example of this what might be called "The Monodromy Theorem," which states that, for certain topological spaces X, there is a triple equivalence between locally constant sheaves on X, covering spaces of X, and sets with an action from the fundamental group of X. This result has been generalized for stratified spaces in a number of directions by a number of people (including David Ayala!). This talk will focus on presenting a particularly clean version called "The Exodromy Theorem," first proved by MacPherson, that remains a source of inspiration for modern research. The Exodromy Theorem states that there is an equivalence between presheaves on the exit-path category of a stratified space Y and constructible sheaves on that same space Y. The talk will conclude with a view of some open questions related to this result and directions for potential research.