Course MAT528

Topics in Nonlinear Analysis: The rigidity, stability, and formation of black holes

The broad objective of the course is to introduce graduate students and advanced undergraduates to some current topics of research in nonlinear partial differential equations, mainly of hyperbolic type, as they appear in General Relativity, Classical, and Relativistic Field theories, such as Yang-Mills and Wave Maps, Fluid Dynamics, Elasticity, etc.  The specific goal will be to introduce some of the recent developments concerning the rigidity and stability and the formation of Black Holes. 


I expect the students enrolling in this course to have a good background in geometry and PDE's.