Stability and moduli spaces

January 9 to January 13, 2017

at the

American Institute of Mathematics, San Jose, California

organized by

Anand Deopurkar, Maksym Fedorchuk, Ian Morrison, and Xiaowei Wang

Original Announcement

This workshop will be devoted to a review of the role played by $K$-stability, Koll\'ar-Shepherd-Barron-Alexeev (KSBA) stability, GIT stability, and Bridgeland stability in the construction and compactification of moduli spaces in algebraic geometry. The organizing theme will be to investigate connections between these flavors of stability, with the goals of incubating new moduli spaces of curves, surfaces, and higher-dimensional varieties and of clarifying the birational geometry of familiar ones. The workshop will bring together experts in stability in all its flavors as well as in moduli theory, minimal model program, differential geometry, and derived categories.

The main topics of the workshop are:

  1. GIT stability for projective varieties, especially pluricanonically polarized ones, and their syzygies.
  2. Notions of stability arising from derived categories and their application to the birational geometry of moduli spaces of varieties and bundles.
  3. K\"ahler-Einstein compactification of moduli of smooth $K$-stable varieties and its algebraization (i.e., smoothable K-polystable compactification).
  4. Connections between asymptotic GIT stability and $K$-stability.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.