Daniele Angella (Università di Firenze)

Abstract: We survey some analytic problems concerning the geometry of the Chern con- nection of Hermitian manifolds: the existence of metrics with constant Chern-scalar curvature; the generalizations of the Kähler-Einstein condition to the non-Kähler setting; the convergence of the normalized Chern-Ricci flow on compact complex surfaces; the asymptotic behaviour of Monge-Ampère volumes of Hermitian metrics in the ddc-class. The talk is based on joint collaborations with Simone Calamai, Mauricio Corrêa, Vincent Guedj, Chinh Lu, Francesco Pediconi, Cristiano Spotti, Valentino Tosatti.