- 09/13/17: Singularities of Hermitian-Yang-Mills connections
- 01/10/17 and 01/12/17: Isolated conical singularities of Calabi-Yau varieties
- 09/9/2016: Degeneration of Calabi-Yau metrics
September 13, 2017
TITLE: Singularities of Hermitian-Yang-Mills connections
ABSTRACT: In this talk we discuss how to understand the tangent cones of Hermitian-Yang-Mills connections in terms of the local algebraic data on the underlying reflexive sheaf. (Joint work with Xuemiao Chen)
January 10, 2017 and January 12, 2017
TITLE: Isolated conical singularities of Calabi-Yau varieties
ABSTRACT: I will talk about joint work with Hans-Joachim Hein on the conical behavior of Ricci-flat metrics on Calabi-Yau varieties with certain types of isolated singularities. Interesting examples include hypersurfaces with nodal singularities. In the more technical part I will try to sketch the main steps involved in the proof.
September 9, 2016
TITLE: Degeneration of Calabi-Yau metrics
ABSTRACT: The complex structure moduli space of Calabi-Yau manifolds can be compactified using the Gromov-Haudorff topology, and a central question is to understand the structure of these Gromov-Hausdorff limits. We will focus on the “non-collapsing” case, and explain the connection with algebraic geometry (joint work with S. Donaldson), and the recent example of a compact Calabi-Yau manifold with isolated conical singularities (joint work with H. Hein). A well-known application of the latter is the existence of special Lagrangian spheres on the smoothing of nodal Calabi-Yau varieties.