Colloquium (special time)

Speaker: 

Duong Phong

Institution: 

Columbia University

Time: 

Tuesday, February 26, 2019 - 4:00pm to 5:00pm

Location: 

RH 306

Since the mid 1990’s, the leading candidate for a unified theory of all fundamental physical interactions has been M Theory.

A full formulation of M Theory is still not available, and it is only understood through its limits in certain regimes, which are either one of five 10-dimensional string theories, or 11-dimensional supergravity. The equations for these theories are mathematically interesting in themselves, as they reflect, either directly or indirectly, the presence of supersymmetry. We discuss recent progresses and open problems about two of these theories, namely supersymmetric compactifications of the heterotic string and of 11-dimensional supergravity. This is based on joint work of the speaker with Sebastien Picard and Xiangwen Zhang, and with Teng Fei and Bin Guo.

Volume estimates for tubes around submanifolds using integral curvature bounds

Speaker: 

Yousef Chahine

Institution: 

UC Santa Barbara

Time: 

Tuesday, December 4, 2018 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

We generalize an inequality of E. Heintze and H. Karcher for the volume of tubes around minimal submanifolds to an inequality based on integral bounds for k-Ricci curvature. Even in the case of a pointwise bound this generalizes the classical inequality by replacing a sectional curvature bound with a k-Ricci bound. This work is motivated by the estimates of Petersen-Shteingold-Wei for the volume of tubes around a geodesic and generalizes their estimate. Using similar ideas we also prove a Hessian comparison theorem for k-Ricci curvature which generalizes the usual Hessian and Laplacian comparison for distance functions from a point and give several applications.

Hermitian manifolds with non-positive curvature

Speaker: 

Man-Chun Lee

Institution: 

UBC

Time: 

Tuesday, February 19, 2019 - 4:00pm

Host: 

Location: 

RH 306

A recent breakthrough of Wu and Yau asserts that a compact projective Kahler 
manifold with negative holomorphic sectional curvature must have ample 
canonical line bundle. In the talk, we will talk about some of the recent 
advances along this direction. In particular, we will discuss the case 
where the manifold is a noncompact Kahler manifold. We will also discuss 
the case when the Kahlerity is a priori unknown. Part of these are joint 
work with S. Huang, L.-F. Tam, F. Tong.

Low Entropy and the Mean Curvature Flow with Surgery

Speaker: 

Alex Mramor

Institution: 

UC, Irvine

Time: 

Tuesday, October 16, 2018 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

In this talk we will discuss the mean curvature flow with surgery and how to extend it to the low entropy, mean convex setting. An application to the topology of low entropy self shrinkers will also be discussed. This is a joint work with Shengwen Wang.

Pages

Subscribe to RSS - Differential Geometry