## Learning Seminar in Geometric Invariant Theory

Dear all,

James Mracek and myself are organizing a learning seminar on Geometric
Invariant Theory in the summer term. GIT (Geometric Invariant Theory) is a
powerful technique that was developed by Mumford in the 1960s to construct
moduli spaces in algebraic geometry. Since then, GIT has emerged as not
only an important tool in algebraic geometry, but also in symplectic
geometry and arithmetic geometry. We plan to cover some subset of the
following topics:

- Different notions of quotients (categorical, good, geometric, etc)
- Reductive Group Actions and Classical Invariant Theory (Hilbert's 14th
problem, etc)
- Linearization of group actions
- Stability and numerical criterion for stability (Hilbert-Mumford criterion)
- Construction of moduli spaces using GIT (moduli of quiver
representations, moduli of genus g curves, etc)
- GIT in symplectic geometry (GIT quotient vs symplectic quotient,
Kahler/hyperkahler quotients; cf. Mumford Chapter 8)
- GIT in arithmetic contexts (abelian schemes)

We plan to use the following sources:

- Dolgachev: Lectures in Invariant Theory
- Mumford/Fogarty/Kirwan: Geometric Invariant Theory
- Mukai: An Introduction to Invariants and Moduli

I would like to have an organizational meeting for all those who are
Kevin