Trading Linearity for Ellipticity: A Nonsmooth Approach to Einstein's Theory of Gravity and the Lorentzian Splitting Theorems

Explore a 42-minute lecture on the nonsmooth approach to Einstein's theory of gravity and Lorentzian splitting theorems. Delve into the Gann Splitting Theorem, Einstein's Theory of Gravity, and geometric concepts including differential geometry and the Riemann curvature tensor. Examine energy conditions, splitting theorems, and challenges in the Lorentzian setting. Gain insights into nonlinear wave operators and develop intuition behind ellipticity. Learn from speaker Robert McCann of the University of Toronto as he presents at the Fields Institute, offering a deep dive into trading linearity for ellipticity in the context of gravitational theory.

Introduction
The Gann Splitting Theorem
Einstein Theory of Gravity
Geometry
Differential Gometry
Reman curvature tensor
Energy con conditions
Splitting theorem
Problems in the Lorentzian setting
Nonlinear wave operators
Intuition behind elliptiicity