# Geometry of algebraic stacks

## Jarod Alper (Australian National University)

Algebraic stacks form a fundamental mathematical structure in algebraic geometry. Specifically, they provide powerful tools to study the equivariant geometry of a group acting on a variety and are indispensable in the study of moduli spaces. This talk will begin with a gentle introduction to algebraic stacks. I will then state a general result on the local geometry of algebraic stacks asserting that essentially every naturally occurring algebraic stack is locally a quotient stack. I will then provide applications of this result to equivariant geometry and to the birational geometry of the moduli space of curves.

Tuesday, November 24th, at 4:00pm in HBH 227

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