Tue May 21, 2013
Inspired by Donaldson's program, we introduce the Kahler Ricci flow with conical singularities. The main part of this talk is to show that the conical Kahler Ricci flow exists for short time and for long time in a proper space. These existence results are hight related to heat kernel and Bessel functions. We will also discuss some...
Tue May 21, 2013
I will discuss natural energy functionals related to the
existence of holomorphic structures on vector bundles and show how
inauspicious Hodge data implies blow up of minimizing sequences.
Grassmann embeddings and an analytic perspective on stability in the
sense of Gieseker and Mumford plays an important role.
Tue May 14, 2013
The classical Kauffman bracket is an invariant of knots in
space. It can be generalized to knots drawn on a surface. I will
discuss surprising properties of these generalized Kauffman
Thu May 2, 2013
We report on recent and ongoing work with Zhou Gang and I.M.
Sigal in which we prove that all MCF neckpinches are asymptotically
rotationally symmetric. Combined with recent work of other authors, this
represents strong evidence in favor of the conjecture that MCF solutions
originating from generic initial data are constrained to one of exactly...
Tue Apr 23, 2013
In the talk, we will explain some joint work with Ovidiu Munteanu
concerning the geometry and analysis of complete manifolds with
Bakry-Emery Ricci curvature bounded from below.
Tue Apr 16, 2013
This is a joint work with Tian. We study the structure of the limit space of a sequence of almost
Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the
initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the
Tue Apr 9, 2013
The uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is biholomorphic to C^n. Perhaps one of reasons that the problem is difficult is lack of examples. Recently assuming U(n) symmetry Wu and Zheng gave a systematic construction on examples of such metrics, we will talk...