Stability and moduli spaces
January 9 to January 13, 2017
American Institute of Mathematics,
San Jose, California
and Xiaowei Wang
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
The main topics of the workshop are:
- GIT stability for projective varieties, especially pluricanonically
polarized ones, and their syzygies.
- Notions of stability arising from derived categories and their application
to the birational geometry of moduli spaces of varieties and bundles.
- K\"ahler-Einstein compactification of moduli of smooth $K$-stable varieties
and its algebraization (i.e., smoothable K-polystable compactification).
- 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.