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Group actions and the cohomology of moduli spaces

Eloise Hamilton
Thursday, June 24, 2021 - 16:30 to 17:30

Moduli spaces play a crucial role in solving classification problems: their geometry encapsulates all of the features of the objects which they classify, and thus questions about the objects can be answered by studying the geometry of the moduli space instead. The aim of this talk is to present some techniques for studying the cohomology of moduli spaces. These techniques require the presence of a group action: either a group action on the moduli space itself, or a group action on a parameter space whose quotient is the given moduli space. I will focus mostly on the latter case, which relates to Geometric Invariant Theory (GIT), and explain how to compute the topology of GIT quotients, both in the classical (reductive) setting and in the recently developed non-reductive setting.

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