Joint UCI-UCSD Seminar: On the conical Kahler Ricci flow

Speaker: 

Yuanqi Wang

Institution: 

UC Santa Barbara

Time: 

Tuesday, May 21, 2013 - 4:00pm

Location: 

RH 340P

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 easy applications of the conical Kahler Ricci flow in conical Kahler geometry.

Complete Kahler manifolds with nonnegative curvature: examples and related results

Speaker: 

Bo Yang

Institution: 

UC San Diego

Time: 

Tuesday, April 9, 2013 - 4:00pm

Location: 

RH 306

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 about some related results.

The regularity of limit space

Speaker: 

Bing Wang

Institution: 

University of Wisconsin-Madison

Time: 

Tuesday, April 16, 2013 - 4:00pm

Location: 

RH 306

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
$L^1$-sense, Ricci curvatures are bounded from below at the initial time. Under the non-collapsed condition, we show that the limit space of a
sequence of almost Einstein manifolds has most properties which is known for the limit space of Einstein
manifolds. As applications, we can apply our structure results to study the
properties of K\"ahler manifolds.

Metrics on surfaces which extremize eigenvalues

Speaker: 

Richard Schoen

Institution: 

Stanford University

Time: 

Monday, February 25, 2013 - 3:00pm

Location: 

RH 306

For closed surfaces and for surfaces with boundary there are natural eigenvalue extremal problems whose solutions, when they exist, determine minimal surfaces in the sphere or the ball with a natural boundary condition. We will discuss the existence problem and describe some geometric properties of extremal metrics.

Singular hermitian metrics and the Hodge conjecture

Speaker: 

Gregory Pearlstein

Institution: 

Michigan State University

Time: 

Tuesday, March 12, 2013 - 4:00pm to 5:00pm

Host: 

Zhiqin Lu

Location: 

RH 306

A Hodge class on a smooth complex projective variety gives rise to an associated hermitian line bundle on a Zariski open subset of a complex projective space P^n.  I will discuss recent work with P. Brosnan which shows that the Hodge conjecture is equivalent to the existence of a particular kind of degenerate behavior of this metric near the boundary.

The Dirichlet problem for the prescribed Ricci curvature equation

Speaker: 

Artem Pulemotov

Institution: 

University of Queensland

Time: 

Thursday, April 4, 2013 - 3:00pm to 4:00pm

Location: 

RH 306

We will discuss the following question: is it possible to find a
Riemannian metric with given Ricci curvature on a manifold $M$? To
answer this question, one must analyze a weakly elliptic
second-order partial differential equation for tensors. In the first
part of the talk, we will review the relevant background and the
history of the subject. After that, our focus will be on new results
concerning the case where $M$ is a bounded domain in a cohomogeneity
one manifold.
 

Universal profiles for mean curvature flow neckpinches

Speaker: 

Dan Knopf

Institution: 

UT Austin

Time: 

Thursday, May 2, 2013 - 4:00pm

Host: 

Jeffrey D. Streets

Location: 

RH 306

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
two asymptotic singularity profiles.

Long time existence of minimizing movement solutions of Calabi flow

Speaker: 

Jeff Streets

Institution: 

UCI

Time: 

Tuesday, February 12, 2013 - 4:00pm

Location: 

RH 306

In 1982 Calabi proposed studying gradient flow of the L^2 norm
of the scalar curvature (now called Calabi flow) as a tool for finding
canonical metrics within a given Kahler class. The main motivating
conjecture behind this flow (due to Calabi-Chen) asserts the smooth long
time existence of this flow with arbitrary initial data. By exploiting
aspects of the Mabuchi-Semmes-Donaldson metric on the space of Kahler
metrics I will construct a kind of weak solution to this flow, known as a
minimizing movement, which exists for all time.

Pages

Subscribe to RSS - Differential Geometry