• • 9/11/2018: Adiabatic limits of anti-self-dual connections on collapsed K3 surfaces
    
  • 4/10/2018: Algebraically special associative submanifolds and special holonomy metrics
    
  • 4/9/2018: On families of special holonomy metrics defined by algebraic curvature condition
  • 9/14/2017: Collapsing of hyperkahler manifolds

September 11, 2018
TITLE: Adiabatic limits of anti-self-dual connections on collapsed K3 surfaces

ABSTRACT: In this talk, we study the convergence of anti-self-dual connections on elliptically fibered K3 surfaces along a collapsing family of Ricci-flat Kahler-Einstein metrics, and show that the restrictions of limit connections on fibers are induced by holomorphic curves. Then we apply the result to a prove a version of Fukaya’s conjecture in the context of SYZ mirror symmetry.

April 10, 2018
TITLE: Collapsing of HyperKahler manifolds

ABSTRACT: This talk is based on the joint work with Valentino Tosatti. We study the collapsing of HyperKahler metrics along holomorphic lagrangian fibrations on projective holomorphic symplectic manifolds

April 9, 2018
TITLE: Collapsing of Calabi-Yau manifolds and special lagrangian submanifolds

ABSTRACT: I will start by introducing the question of collapsing of Ricci-flat Kahler-Einstein metrics when Calabi-Yau manifolds approaching to a certain large complex structure limit. Then I will show the existence of special lagrangian tori in the sufficiently collapsed region of polarized Ricci-flat Calabi-Yau manifolds.

September 14, 2017
TITLE: Collapsing of hyperkahler manifolds

ABSTRACT: In this talk, we study the collapsing of hyperkahler metrics on projective holomorphic symplectic manifolds along holomorphic Lagrangian fibrations. We prove that the Gromov-Hausdorff limits are compact metric spaces, which are half-dimensional special Kahler manifolds outside singular sets of real Hausdorff codimension 2.