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 nonnegative Ricci curvature and almost 
9:00am to 10:00am  Zoom  Inverse Problems Gitta Kutyniok  (LudwigMaximiliansUniversität München) TBA 
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) LocalGlobal Phenomena for Elliptic Curves
A localglobal principle is a result that allows us to deduce global information about an object from local information. A wellknown example is the HasseMinkowski 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 localglobal principles in arithmetic geometry, highlighting two that are related to elliptic curves, one for torsion and one for isogenies. In contrast to the HasseMinkowski 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. 