The primary theme of this special research semester is to explore recent advancements in the theory of complex manifolds, with a focus on both Kählerian and non-Kählerian cases. The semester will begin with a two-week summer school. In the first week, we aim to provide junior participants with foundational training in Calabi-Yau theory within complex geometry. The second week will delve into more advanced topics. Following the summer school, we will host two workshops: one dedicated to Kähler geometry, and the other to non-Kählerian geometry.
Regarding specific research directions, on the classical Kählerian side, we plan to engage in discussions on non-Archimedean aspects of the SYZ conjecture, pluripotential theoretic approaches to singular Kähler-Einstein metrics, and Calabi-Yau metrics on non-compact manifolds. On the non-Kählerian side, key topics will include cohomological properties of complex and symplectic manifolds, analytic techniques in non-Kähler geometry, almost-complex and symplectic structures, deformations of complex objects, topological aspects of complex and symplectic manifolds, and Hodge theory on almost-Hermitian manifolds.
Summer school I: Invitation to complex geometry
(08/04/2025- 08/08/2025)Summer school II: Summer school on singular Kählerian metrics and Hermitian geometry
(08/11/2025- 08/15/2025)Workshop on Singular canonical Kähler metrics on compact and non-compact manifolds
(09/01/2025- 09/05/2025)Workshop on Cohomological and metric aspects of Hermitian and almost complex manifolds
(09/08/2025- 09/12/2025)