MARGE 4
New directions in complex geometry

March 9

15:30 Guilherme Cerqueira Gonçalves

Title: Singular Gauduchon Conjecture

Abstract: In 1984 Gauduchon conjectured that one can find Gauduchon metrics with prescribed Ricci curvature on all compact complex manifolds. This conjecture was settled by Székelyhidi-Tosatti-Weinkove in 2019. In this talk I will present a singular version of this conjecture for degenerating families and discuss a few first results towards its solution. I will describe the (n-1) Monge-Ampère equation, fully non-linear elliptic PDE at the heart of this problem. As time allows I will prove that the potential for a degenerate (n-1) Monge-Ampère equation on a compact Hermitian smoothable variety with canonical isolated singularities is uniformly bounded and that on the holomorphic deformation of a Kähler Calabi-Yau manifold we can construct a non-Kähler Calabi-Yau-Gauduchon metrics, inside fixed Gauduchon classes, with uniform bounds independent of the complex structure.

March 10

09:00 Café

09:30 Yuetong Fang

Title: TBA

Abstract: TBA

10:30 Andrés Moreno

Title: Flows of SU(n)-structures

Abstract: As part of a general approach to the study of flows of H-structures, in this talk we discuss the case when the structure group is H=SU(n). In particular, we focus on the negative gradient flow of a natural Dirichlet-type energy functional and on a coupled Ricci harmonic flow of SU(n)-structures. For those flows, we characterize the critical points, we prove short-time existence and uniqueness as well as Shi-type estimates and long-time existence of solutions of the Ricci harmonic flow of SU(n)-structures. This is a joint work with U. Fowdar (Univ. Warsaw), E. Loubeau (Univ. Brest) and H. Sá Earp (Unicamp).

13:30 Quentin Peres

Title: TBA

Abstract: TBA

14:30 Yifan Chen

Title: TBA

Abstract: TBA

16:00 Antonio Trusiani

Title: TBA

Abstract: TBA

March 11

09:00 Informal discussions