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Non-archimedean integration on quotients

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EMG - New equivariant methods in algebraic and differential geometry

Motivated by mirror symmerty, Batyrev defines ‘stringy’ Hodge numbers for a variety X with Gorenstein canonical singularities using motivic integration. While in general it is an open question, whether these numbers are related to a cohomology theory, the orbifold formula shows, that if X has quotient singularities, they agree with Chen-Ruan’s orbifold Hodge numbers. I will explain how to generalize this orbifold formula to quotients of smooth varieties by linear algebraic groups. As an application we obtain identifications of stringy Hodge numbers with enumerative invariants, so-called BPS -invariants, in the case when X is the moduli space of a category of homological dimension 1. This is joint work with Michael Groechenig and Paul Zigler.

This talk is part of the Isaac Newton Institute Seminar Series series.

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