Mathematics Colloquia and Seminars

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Generalizing the monodromy equivalence, the exodromy equivalence says that the ∞-category of constructible sheaves on a nice enough stratified space (X, P) is equivalent to functors out of the exit-path ∞-category of (X, P). Up until recently, the meaning of “nice enough” was quite restrictive; specifically, the exodromy theorem required the stratification of X to be conical. Unfortunately, many stratifications naturally arising in geometry are not conical. In this talk, we’ll discuss joint work with Mauro Porta and Jean-Baptiste Teyssier that allows us to extend the exodromy theorem to a much larger class of stratified spaces. Examples include: stratifications that can be locally refined by conical stratifications, subanalytic stratifications of real analytic spaces, and algebraic stratifications of real varieties. We’ll also explain some applications, such as representability results for moduli of constructible and perverse sheaves.