Pretalk Title: Fundamentals of Geometric Invariant Theory
Pretalk Abstract: Geometric Invariant Theory (GIT) is a powerful theory for constructing and studying the geometry of moduli spaces in algebraic geometry. In this pretalk I will try to give an overview of the fundamentals of GIT.
Talk Title: Quotients for linear algebraic group actions via Geometric Invariant Theory
Talk Abstract: Given a linear algebraic group acting on a variety, finding a suitable quotient in the category of varieties is typically a non-trivial task. Geometric Invariant Theory (GIT) is a powerful theory for constructing such quotients, provided the group is reductive. When the group is unipotent (in particular non-reductive), the theory of locally nilpotent deviations can be used instead to construct quotients under suitable assumptions. After reviewing the reductive and unipotent approaches, I will explain how they can be combined into a so-called Non Reductive GIT which enables the construction of quotients for possibly non-reductive group actions. Finally (and time permitting) I will list some applications to the construction and study of old and new moduli spaces.