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.

The degenerate special Lagrangian equation on Riemannian manifolds.

Speaker: 

Matthew Dellatorre

Institution: 

University of Maryland

Time: 

Tuesday, November 13, 2018 - 4:00pm

Location: 

RH 306

We show that the degenerate special Lagrangian equation (DSL), recently introduced by Rubinstein–Solomon, induces a global equation on every Riemannian manifold, and that for certain associated geometries this equation governs, as it does in the Euclidean setting, geodesics in the space of positive Lagrangians. For example, geodesics in the space of positive Lagrangian sections of a smooth Calabi–Yau torus fibration are governed by the Riemannian DSL on the base manifold. We then develop their analytic techniques, specifically modifications of the Dirichlet duality theory of Harvey–Lawson, in the Riemannian setting to obtain continuous solutions to the Dirichlet problem for the Riemannian DSL and hence continuous geodesics in the space of positive Lagrangians

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