Title: Fixed point loci in moduli problems

Abstract: Whenever a smooth variety X admits the action of a torus T, the Atiyah-Bott localization formula allows reducing computations in the cohomology of X to computations on the fixed locus X^T. This is particularly powerful when X^T is more explicit than X, as it is often the case in moduli theory.

In my talk, I will explain why in the context of localization, it is essential to work with the moduli stack as opposed to the moduli space, and I will discuss joint work with J. Alper that describes the global structure of torus fixed loci in algebraic stacks.