Complete noncompact Kaehler manifolds with positive curvature

Speaker: 

Xi-Ping Zhu

Institution: 

Sun Yat-sen University

Time: 

Tuesday, August 6, 2019 - 4:00pm

Location: 

RH 306

The well-known Yau’s uniformization conjecture states that any
complete noncompact Kaehler manifold with positive bisectional curvature is
bi-holomorphic to the complex Euclidean space. The conjecture for the case
of maximal volume growth has been recently confirmed by G. Liu. In this
talk, we will consider the conjecture for manifolds with non-maximal volume
growth. We will show that the finiteness of the first Chern number is an
essential condition to solve Yau’s conjecture by using algebraic embedding
method. Furthermore, we can verify the finiteness in the case of minimal
volume growth. In particular, we obtain a partial answer to Yau’s
uniformization conjecture on complex two-dimensional Kaehler manifolds with
minimal volume growth. This is a joint work with Bing-Long Chen.

Location of hot spots in thin curved strips

Speaker: 

David Krejcirik

Institution: 

Czech Technical University in Prague

Time: 

Tuesday, June 25, 2019 - 4:00pm

Host: 

Location: 

RH 306

According to the conjecture of Rauch’s from 1974, any eigenfunction corresponding to the principal eigenvalue of the Neumann Laplacian attains its extrema on the boundary of planar domains. After giving an account on the history and validity of the conjecture, we present our own new results for tubular neighbourhoods of curves on surfaces. This is joint work with Matej Tusek.

Entropy, noncollapsing, and a gap theorem for ancient solutions to the Ricci flow

Speaker: 

Yongjia Zhang

Institution: 

UC San Diego

Time: 

Tuesday, May 21, 2019 - 4:00pm

Location: 

RH 306

Entropy has been an important topic in the study of Ricci flow
ever since it was invented by Perelman. We consider Perelman's entropy
defined on an ancient solution, and prove a gap theorem for its backward
limit: If Perelman's entropy limits to a number too close to zero as time
approaches negative infinity, then the ancient solution must be the trivial
Euclidean space.

UCI-UCR-UCSD Joint Differential Geometry Seminar

Institution: 

Joint seminar

Time: 

Tuesday, June 4, 2019 - 4:00pm to 6:00pm

Location: 

UC Riverside Skye 347

Location: Skye Hall 347

 

4:00-4:50pm

Speaker: Yu-Shen Lin (Boston University)

Title: Special Lagrangian fibrations in weak Del Pezzo Surfaces

Abstract: Motivated by the study of mirror symmetry, Strominger-Yau-Zaslow (SYZ) conjectured that Calabi-Yau manifolds admit certain minimal Lagrangian fibrations. These minimal Lagrangians are the special Lagrangian submanifolds studied earlier by Harvey-Lawson. Many of the implication of the SYZ conjecture is proved and it has been the guiding principle for studying mirror symmetry for a long time. However, not many special Lagrangians are known in the literature. In this talk, I will prove the existence of special Lagrangian fibration on the complement of a smooth anti-canonical divisor in a (weak) Del Pezzo surface. If the time allows, I will explain its impact to mirror symmetry. This is joint work with Tristan Collins and Adam Jacob.

 

5:00-5:50pm

Speaker: Yannis Angelopoulos (UCLA)
Title: Linear and nonlinear waves on extremal Reissner-Nordstrom spacetimes 

Abstract:  I will present several results (that have been obtained jointly with Stefanos Aretakis and Dejan Gajic) from the analysis of solutions of linear and nonlinear wave equations on extremal Reissner-Nordstrom spacetimes, including sharp asymptotics on the horizon and at infinity for linear waves, and instability phenomena for nonlinear waves. These results can be seen as stepping stones to the fully nonlinear problem of stability/instability of extremal black holes.

 

Ancient and translating solutions to mean curvature flow

Speaker: 

Mat Langford

Institution: 

University of Tennessee

Time: 

Tuesday, April 9, 2019 - 4:00pm

Host: 

Location: 

RH 306

A deep result of X.-J. Wang states that a convex ancient solution to mean curvature flow either sweeps out all of space or lies in a stationary slab (the region between two fixed parallel hyperplanes). We will describe recent results on the construction and classification of convex ancient solutions and convex translating solutions to mean curvature flow which lie in slab regions, highlighting the connection between the two. Work is joint with Theodora Bourni and Giuseppe Tinaglia.

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