Stability conditions on noncommutative varieties and the geometry of moduli spaces
Data: 08 APRILE 2025 dalle 11:15 alle 13:00
Luogo: aula Seminario VIII piano, ore 11:15
Abstract: In his celebrated work, Mumford introduced the notion of slope stability for vector bundles on curves, leading to the construction of projective varieties parametrizing semistable bundles of fixed rank and degree. Since then, these results have been generalized to higher dimensional varieties and coherent sheaves with outstanding applications in algebraic geometry and differential geometry.
A further breakthrough is due to Bridgeland, who considered the more abstract context of triangulated categories and defined the concept of stability for objects therein. In fact, this notion of stability recovers slope stability when considering the bounded derived category of a smooth projective curve.
The goal of this talk is to give a gentle introduction to the recent progresses in the theory of stability conditions and moduli spaces with particular focus on the applications in hyperkahler geometry.