EVENT DETAILS AND ABSTRACT

Title: An introduction to geometry, analysis, and the nonlinear harmonic map equation
Speaker: Aaron Naber
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

In this talk we begin by introducing many basic concepts and classical ideas, including Riemannian manifolds, curvature, the linear laplace operator, and their applications to topology. A standard and important class of nonlinear equations on such spaces are the harmonic maps between Riemannian manifolds, which are the natural nonlinear analogues of the linear laplacian. Despite a large amount of work in the area, Schauder estimates for solutions of the nonlinear harmonic map equation, which are completely standard in the linear case, were only proved in the last couple years. The last part of the talk will outline the proof of these estimates.