"(Hermitian)-Yang-Mills connections in higher dimensions"

by Prof. Wentworth Richard

Tuesday 24 Jan 2023, 17:00 → 18:00 Europe/Berlin

H4 (Geomatikum)

Abstract: Energy minimizing connections in dimension four (instantons) have played an important role in physics and mathematics since the '70s. More recently, higher dimensional versions of Yang-Mills connections
are being used to study manifolds with special holonomy. In the context of complex geometry, solution spaces of these equations are closed related to moduli spaces of holomorphic objects subject to stability conditions.
This talk will partly survey developments in this area. I will also discuss more recent results, such as the existence of suitably singular Hermitian-Einstein metrics on normal projective varieties that are smooth in codimension two. A particular application is a characterization of those sheaves
that saturate the Bogomolov-Gieseker inequality.