# Mathematics Algebra Seminar: Hannah Dell, Stability conditions on free quotients

This event is in the past.

**When:**

March 19, 2024

1 p.m. to 2 p.m.

1 p.m. to 2 p.m.

**Where:**

**Event category:**Seminar

In-person

Speaker: Hannah Dell from the University of Edinburgh

**Title**: Stability conditions on free quotients

**Abstract**: Bridgeland stability conditions have been constructed on curves, surfaces, and in some higher dimensional examples. In several cases, there are only so-called “geometric” stability conditions which are constructed using slope stability for sheaves, whereas in other cases there are more (e.g. coming from an equivalence with representations of a quiver). Lie Fu -- Chunyi Li -- Xiaolei Zhao were the first to provide a general result explaining this phenomena. In particular, they showed that if a variety has a finite map to an abelian variety, then all stability conditions are geometric. In this talk, we test the converse on surfaces that arise as free quotients by finite groups. To do this, we will develop a method to study stability conditions on any triangulated category with a group action. This is joint work with Edmund Heng and Tony Licata.