Stable Horizons and the Penrose Conjecture

Speaker: 

Henri Roesch

Institution: 

UC Irvine

Time: 

Tuesday, March 6, 2018 - 4:00pm to 5:00pm

Location: 

RH 306

In the first half of the talk, we introduce a new quasi-local mass with interesting properties along null flows off of a 2-sphere in spacetime or, equivalently, foliations of a null cone. We also show how certain, fairly generic, convexity assumptions on the null cone allows for a proof of the Penrose Conjecture. On the Black Hole Horizon, we find that the convexity assumptions become sharp; therefore, the second half of the talk will explore the existence of a class of Black Hole Horizons admitting such convexity. From this, building upon the work of S. Alexakis, we will show that the Schwarzschild Null Cone--the case of equality for the Penrose Conjecture--is also critical in light of recent work on the perturbation of stable, weakly isolated Horizons.

 

 

On Hamiltonian Gromov-Witten theory for symplectic reductions

Speaker: 

Rui Wang

Institution: 

UC Irvine

Time: 

Tuesday, November 7, 2017 - 4:00pm

Location: 

RH 306

In this talk, I will first review our work on defining a new quantum deformation for the (Chen-Ruan) cohomology ring of a symplectic reduction. Then I will explain the relation between this quantum deformation and the well-known quantum cohomology ring. Our construction is based on the study of moduli spaces of symplectic vortices with proper metrics. This is a joint project with B. Chen and B. Wang.

Algebraic Gluing of Holomorphic Discs in K3 Surfaces and Tropical Geometry

Speaker: 

Yu-Shen Lin

Institution: 

Harvard CMSA

Time: 

Monday, October 30, 2017 - 4:00pm

Location: 

RH 340P

We will start from the motivation of the tropical geometry. Then
we will explain how to use Lagrangian Floer theory to establish the
correspondence between the weighted counting of tropical curves to the
counting of holomorphic discs in K3 surfaces. In particular, the result
provides the existence of new holomorphic discs which do not come easily
from direct gluing argument.

 

 

Minimizers of the sharp Log entropy on manifolds with non-negative Ricci curvature and flatness

Speaker: 

Qi Zhang

Institution: 

UC Riverside

Time: 

Tuesday, November 21, 2017 - 4:00pm

Host: 

Location: 

RH 306

Consider the scaling invariant, sharp log entropy (functional)
introduced by Weissler on noncompact manifolds with nonnegative Ricci
curvature. It can also be regarded as a sharpened version of
Perelman's W entropy  in the stationary case. We prove that it has a
minimizer if and only if the manifold is isometric to $\R^n$.
Using this result, it is proven that a class of noncompact manifolds
with nonnegative Ricci curvature is isometric to $\R^n$. Comparing
with some well known flatness results in on asymptotically flat
manifolds and asymptotically locally Euclidean (ALE) manifolds, their
decay or integral condition on the curvature tensor is replaced by the
condition that the metric converges to the Euclidean one in C1 sense
at infinity. No second order condition on the metric is needed.

Tangent cones of Yang-Mills connections with applications to G2 instantons

Speaker: 

Adam Jacob

Institution: 

UC Davis

Time: 

Tuesday, February 27, 2018 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

The study of tangent cones in geometric analysis is an important tool in understanding the structure at a singular point of a geometric equation. In this talk I will discuss how to uniquely identify the tangent cone of a Yang-Mills connection with isolated singularity in the complex setting, given an initial assumption on the complex structure of the bundle. I will then discuss applications to a project with the goal of constructing examples of singular G2 instantons, using the twisted connected sum construction. This is joint work with H. Sa Earp and T. Walpuski.

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