Title: Nearby cycles over general bases and connections to Springer theory
Abstract: The study of nearby cycles has long been fruitful in characterizing degenerations of algebraic varieties and in describing singularities that can appear in models over discrete valuation rings. In this talk I will explain how one can work with nearby cycles from the point of view of singularities in characteristic p, discuss some modern developments regarding their perversity and variation in families over general bases, and examine some connections to a rich source of singularities coming from a representation-theoretic background via Springer theory. If time permits, we will see how p-adic nearby cycles can be more pathological than their l-adic counterparts, along with a technique that can remedy some of their pathologies.
Yuchen Liu
(847) 491-5553
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