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.

Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces

Speaker: 

Jeff Viaclovsky

Institution: 

UC Irvine

Time: 

Tuesday, October 2, 2018 - 4:00pm

Location: 

RH 306

I will discuss a new construction of families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding singular fibration from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds. This is joint work with Hans-Joachim Hein, Song Sun, and Ruobing Zhang.

Strictly pseudoconvex domains in C^2 with obstruction flat boundary

Speaker: 

Sean Curry

Institution: 

UC San Diego

Time: 

Tuesday, October 30, 2018 - 4:00pm

Location: 

RH 306

A bounded strictly pseudoconvex domain in C^n, n>1, supports a
unique complete Kahler-Einstein metric determined by the Cheng-Yau solution
of Fefferman's Monge-Ampere equation. The smoothness of the solution of
Fefferman's equation up to the boundary is obstructed by a local CR
invariant of the boundary called the obstruction density. In the case n=2
the obstruction density is especially important, in particular in describing
the logarithmic singularity of the Bergman kernel. For domains in C^2
diffeomorphic to the ball, we motivate and consider the problem of
determining whether the global vanishing of this obstruction implies
biholomorphic equivalence to the unit ball. (This is a strong form of the
Ramadanov Conjecture.)

Convex hypersurface theory in higher-dimensional contact topology

Speaker: 

Ko Honda

Institution: 

UCLA

Time: 

Tuesday, November 20, 2018 - 4:00pm

Location: 

RH 306

Convex surface theory and bypasses are extremely powerful tools
for analyzing contact 3-manifolds.  In particular they have been
successfully applied to many classification problems.  After reviewing
convex surface theory in dimension three,  we explain how to generalize many
of their properties to higher dimensions.   This is joint work with Yang
Huang.

The Minkowski formula and the quasi-local mass

Speaker: 

Po-Ning Chen

Institution: 

UC Riverside

Time: 

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

Location: 

RH 306

In this talk, we will discuss the relationship between the Minkowski formula and the quasi-local mass in general relativity, In particular, we will use the Minkowski formula to estimate the quasi-local mass. Combining the estimate and the positive mass theorem, we obtain rigidity theorems which characterize the Euclidean space and the hyperbolic space.

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