Andres Fernandez Herrero (U Penn)
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PDL C-401
Abstract: This series of lectures aims to introduce the audience to some recent tools in the construction of good moduli spaces for stacks.
We will begin with a brief introduction to Halpern-Leistner's theory of Theta-stability. We will then discuss "Infinite dimensional GIT", which is a technique to prove the existence of good moduli spaces for the semistable loci of certain stability conditions. Throughout the lecture series, our guiding example will be the moduli problem of decorated principal bundles on a smooth projective curve. If time allows, I will also explain how to use these techniques to obtain compact moduli spaces of decorated vector bundles for families of nodal curves.