for this workshop
Stability and moduli spaces
American Institute of Mathematics, San Jose, California
Anand Deopurkar, Maksym Fedorchuk, Ian Morrison, and Xiaowei Wang
This workshop, sponsored by AIM and the NSF, will be devoted to a review of the role played by $K$-stability, Kollár-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:
- 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.
- Kähler-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.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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