EVENT DETAILS AND ABSTRACT

Title: Regularity and Break-down in Geometric Field Theories
Speaker: Professor Shadi Tahvildar-Zadeh
Speaker Info: Princeton University
Brief Description:
Special Note:
Abstract:

This is a survey talk about a variety of issues that arise in geometric field theories. While the ultimate goal of any study in this area remains to be the understanding of global existence, break-down and large-time behavior of solutions of the physically relevant field theories such as General Relativity and Yang-Mills, valuable insight can be gained by first focusing on {\em wave maps}: A simpler, less physical, field theory which exhibits many similarities with the above, and in which many of the hidden difficulties in dealing with those physical theories are present in a more transparent way. Wave maps are the hyperbolic analogue of harmonic maps between manifolds, where the domain instead of being Riemannian is Lorentzian. They thus satisfy a system of semilinear wave equations with a quadratic nonlinearity in the gradient. After introducing the conservation laws associated with the wave map system, the following problems will be discussed: (1) Global existence of classical solutions, (2) Asymptotic behavior, (3) Formation of singularities.