73rd Midwest PDE Seminar, May 10-11, 2014

Northwestern University, Evanston IL

Investigators

Abstract

The Midwest PDE Seminar is a conference series that has been held biannually since 1977 at universities across the Midwest. Partial Differential Equations (PDE) are ubiquitous throughout science and engineering, since they express relationships between rates of change of quantities of interest. Linear PDE such as Laplace, heat, wave, and Schrödinger equations are central to many phenomena in physics. Nonlinear PDE arise in fields such as general relativity, condensed matter physics and optics, gauge field theory, and fluid dynamics. Nonlinear PDE are also employed to tackle mathematical problems in the area of geometric analysis. This meeting brings together experts from across these fields to exchange information about recent research results and to foster collaborative research. This award provides partial support for the 73rd edition of the Midwest PDE Seminar, to be held at Northwestern University on the weekend of May 10-11, 2014. Study of the Laplace, heat, wave, and Schrödinger equations remains a lively and rich subject; for instance the study of Laplace eigenfunctions and eigenvalues in both compact and noncompact settings (spectral and scattering theory) is of considerable current interest. Moreover, nonlinear PDE such as arise in general relativity (Einstein equations), condensed matter physics and optics (nonlinear Schrödinger equation), gauge field theory (Yang-Mills equations), and fluids (Navier-Stokes and Euler equations) remain rich in mysteries. On the side of geometry, the study of Riemannian manifolds endowed with special metrics has seen astounding advances in recent years. Work involving Hamilton's Ricci flow and breaking developments in the theory of Kähler-Einstein metrics on Fano manifolds have involved profound new tools from PDE. These theories are tied to a nonlinear degenerate parabolic equation (Ricci flow) and an elliptic equation (complex Monge-Ampère) respectively. Discussions in this seminar will address these and other topics. The conference encourages and supports broad and diverse participation of junior mathematicians, women, and underrepresented minorities. Conference web site: http://www.math.northwestern.edu/midwestpde/