Abstract

Gauduchon metrics are very useful generalizations of Kähler metrics in non-Kähler geometry, as Gauduchon proved that these special metrics always exist on compact complex manifolds. One of their important applications is defining the notion of stability for vector bundles/sheaves on non-Kähler manifolds. It also leads to studying the existence of Hermite-Einstein metrics and the classification of non-Kähler surfaces. In this talk, I will first introduce a singular version of Gauduchon's theorem and its application to the Hermite-Einstein problem for stable reflexive sheaves on non-Kähler normal varieties. Then, I will explain one of the main technical points that lies in obtaining uniform Sobolev inequalities for perturbed hermitian metrics on a resolution of singularities. 

Brief biography

Chung-Ming Pan is currently a postdoc at Université du Québec à Montréal. He obtained his Ph.D. at Université de Toulouse in 2023 under the supervision of Vincent Guedj and Henri Guenancia. His research focuses on complex geometry and differential geometry. 

Zoom meeting

Link                   ID: 890 7805 9254                     Password: 212868