Week of March 7, 2021

Tue Mar 9, 2021
3:00pm to 4:00pm - Zoom - Analysis
Arunima Bhattacharya - ( University of Washington, Seattle)
Hessian Estimates for the Lagrangian mean curvature equation

In this talk, we will discuss a priori interior estimates for the Lagrangian mean curvature equation under certain natural restrictions on the Lagrangian phase. As an application, we will use these estimates to solve the Dirichlet problem for the Lagrangian mean curvature equation with continuous boundary data on a uniformly convex, bounded domain.

 

4:00pm - Zoom - Differential Geometry
Guoyi Xu - (Tsinghua University)
The construction of the splitting maps

For a geodesic ball with non-negative Ricci curvature and almost
maximal volume, we give the existence proof of splitting map without
compactness argument. There are two technical new points, the first one is
the way of finding n-directional points by induction and stratified Gou-Gu
Theorem, the second one is the error estimates of projections. The content
of the talk is technical, but we will explain the basic geometric intuition
behind the technical proof. This is a joint work with Jie Zhou.

Thu Mar 11, 2021
9:00am to 10:00am - Zoom - Inverse Problems
Gitta Kutyniok - (Ludwig-Maximilians-Universität München)
TBA

https://sites.uci.edu/inverse/

10:00am to 11:00am - - Mathematical Physics
Maximilian Pechmann - (University of Tennessee, Knoxville)
tba
3:00pm to 4:00pm - Zoom: https://uci.zoom.us/j/95528784206 - Number Theory
Jacob Mayle - (University of Illinois, Chicago)
Local-Global Phenomena for Elliptic Curves

 

A local-global principle is a result that allows us to deduce global information about an object from local information. A well-known example is the Hasse-Minkowski theorem, which asserts that a quadratic form represents a number if and only if it does so everywhere locally. In this talk, we'll discuss certain local-global principles in arithmetic geometry, highlighting two that are related to elliptic curves, one for torsion and one for isogenies. In contrast to the Hasse-Minkowski theorem, we'll see that these two results exhibit considerable rigidity in the sense that a failure of either of their corresponding everywhere local conditions must be rather significant.