# Jarod Alper: Valuative criteria for moduli problems

**Time: **
Wed 2018-09-19 13.15 - 15.00

**Lecturer: **
Jarod Alper (University of Washington)

**Location: ** Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

We will discuss various valuative criteria for algebraic stacks that hold for many moduli problems parameterizing objects that may have positive dimensional stabilizers (eg. semistable vector bundles over a curve). We have three applications in mind: (1) existence of Cartan—Iwahori decompositions for reductive groups, (2) semistable reduction theorems for moduli problems, and (3) existence of moduli schemes/algebraic spaces parameterizing objects up to S-equivalence.

This is joint work with Daniel Halpern-Leistner and Jochen Heinloth.