# General Relativity and Cosmology

## General Relativity, Differential Geometry and Differential Equations; Stories From a Successful Menage-a-trois

**N.B. Due to problems with the microphone, the audio quality of this video is significantly lower than expected.**

It is well known that Einstein's general theory of relativity provides a geometrical description of gravity in terms of space-time curvature. Einstein's theory poses some fascinating and difficult mathematical challenges that have stimulated a great deal of research in geometry and partial differential equations. Important questions include the well-posedness of the evolution problem, the definition of mass and angular momentum, the formation of black holes, the cosmic censorship hypothesis, the linear and non-linear stability of black holes and boundary value problems at conformal infinity arising in the analysis of the AdS/CFT correspondence. I will give a non-technical survey of some significant advances and open problems pertaining to a number of these questions.

## String Theory Compactification with/without Torsion

Topics:

• Geometry and Holomony

• Supersymmetry, Spinors, and Calabi-Yau

• Flux and Backreaction

• Energetics of Heterotic Flux Compactification

• Strominger System and Heterotic Flux as a Torsion

• A Supersymmetric Solution to Heterotic Flux Compactification

• Global Issues: Index Counting, Smoothness, etc