SUN Jun (Wuhan University)

Sphere theorems for submanifolds in Kahler manifold
Abstract: In this talk, we will first recall the previous results on topological and differentiable sphere theorems. Then we will talk about our recent results on sphere theorems for submanifolds in Kahler manifold. This is joint work with Linlin Sun.

SHI Yalong (Nanjing University)

Some collapsing estimates for normalized Kahler-Ricci flow
Abstract: I shall talk about my recent joint work with Wangjian Jian on the higher order estimates for a collapsing family of metrics on certain Kahler manifolds and for collapsing Calabi-Yau metrics.

SJÖSTRÖM DYREFELT Zakarias (ICTP)

Optimal lower bounds for Donaldson's J-functional
Abstract: We give an explicit formula for precisely how far Donaldson's J-functional is from being proper, and show that for surfaces the optimal lower bound is an explicitly computable rational function in the underlying Kähler class. We also discuss a number of applications to Calabi dream manifolds and an analogous notion for the J-equation, new sufficient criteria for existence of cscK metrics in terms of Tian's alpha invariant, and show existence of optimal degenerations for uniform J-stability on manifolds satisfying the Lejmi-Székelyhidi conjecture.