Daniele Angella: Chern Ricci flow on compact complex surfaces
Eleonora Di Nezza: Singular Kähler-Ricci flow
In this talk, we provide a detailed analysis of the singularities arising in the Kähler-Ricci flow on a compact Kähler manifold when the initial data is given by the current of integration along a divisor.
We prove that the smoothing occurs through a progressive transition: the initial divisorial singularities are gradually replaced by singularities of Poicaré type.
This is a joint work with V. Guedj and C. Lu.
Mario Garcia-Fernandez: TBA
Giovanni Gentili: Recent developments in HKT geometry
In 2010, Alesker and Verbitsky formulated a quaternionic analogue of the Calabi conjecture for compact hyperkähler manifolds with torsion (HKT manifolds). Assuming that the canonical bundle is holomorphically trivial, the conjecture would imply the existence of a balanced and Chern–Ricci-flat HKT metric. In this talk, I will survey the current state of the art on the conjecture and related problems, focusing primarily on two recent solvability results obtained in collaboration with Luigi Vezzoni (arXiv:2610.07897) and with Antonio Trusiani and Luigi Vezzoni (arXiv:2609.21528).
Lorenzo Foscolo: TBA
Sebastien Picard: Special Lagrangian submanifolds and circle collapse on K3
We consider Foscolo’s construction of K3 surfaces degenerating to a three-dimensional affine base. We discuss how straight lines on the base lift to degenerating sequences of special Lagrangian two-spheres and tori. The proof involves a gluing construction of compact special Lagrangians. This is joint work with Federico Trinca.
Nicoletta Tardini: TBA