Time:10:00-11:30am, June 19，20，26 and 27, 2023

Abstract: 

In this mini-course, we will give a short introduction to the theory of Bridgeland stability conditions, which was motivated from string theory. This theory turns out to be related to many dierent branches of mathematics. For example, algebraic geometry, representation theory, symplectic geometry, curve counting theories, and more recently, p-adic geometry.

The plan is following:

Lecture 1: We briefly introduce the basic notion and theorems in the theory of Bridgeland stability conditions. This is based on [Bri07] and [KS08].

Lecture 2: We give the construction of Bridgeland stability conditions on surfaces and product varieties. This is based on [AB13] and [Liu21].

Lecture 3: We introduce the theory of stability conditions on cyclic categories (triangulated categories with [2] = [0]). This is based on [Liu22].

Lecture 4: We discuss its possible application on Fargues-Fontaine curves (both archimedean and non-archimedean ones). This is based on an ongoing work joint with Heng Du and Qingyuan Jiang.