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## Moduli problems beyond geometric invariant theory

January 25 to January 29, 2021

at the

American Institute of Mathematics, San Jose, California

organized by

Jarod Alper, Daniel Halpern-Leistner, Yuchen Liu, and Filippo Viviani

This workshop, sponsored by AIM and the NSF, will be devoted to applications of recent foundational developments in the theory of algebraic stacks (constructions of moduli spaces and generalizations of Harder-Narasimhan theory) to specific moduli problems of long-standing interest, such as the moduli of curves, the moduli of higher dimensional varieties and the moduli of principal bundles. This workshop will bring together experts in each of these moduli problems.

The workshop will focus on the following particularly promising applications:

1. Stability conditions for singular curves and the minimal model program for $M_g.$

2. Theta-stratifications and wall crossings for moduli spaces of Fano varieties

3. Moduli of singular principal $G$-bundles and compactifications of the universal $G$-bundle over stable curves.

This event will be run as an AIM-style workshop. 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.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than December 5, 2020. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.