Description:

We are organizing a study seminar between the universities of Bologna, Chemnitz and Nancy, with the goal of understanding Bridgeland stability conditions. This is a framework which provided far-reaching results in the theory of moduli spaces and beyond: in the original paper by Bridgeland the space of stability conditions on a given category has been proven to be a (possibly infinite-dimensional) manifold while in further works by Bayer and Macrì the moduli space of stable objects on a K3 surface (with some generality assumptions) has been shown to be projective, and applications to the birational geometry of certain hyperkähler varieties have been found. The main objective of our seminar is to make it all the way to proving Theorem 1.3 in the paper Projectivity and Birational Geometry of Bridgeland moduli spaces by Arend Bayer and Emanuele Macrì.

The present formulation of Bridgeland stability conditions is a well established theory, our plan is to present it with a self-contained series of talks spanning the whole fall semester. We will start with a gentle introduction on triangulated and derived categories and we will cover the necessary information to understand moduli spaces and stacks.

We are uploading videos of the talk, which are available on YouTube via the links in the table. For privacy reasons the videos' visibility is set to "private". Therefore, if you are interested in watching them, you can ask any of the organizers to be granted access.

Program:

Organizers:

• Simone Billi
• Francesco Denisi
• Franco Giovenzana
• Annalisa Grossi
• Mihai-Cosmin Pavel
• Marco Rampazzo