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: www.math.northwestern.edu/midwestpde/
The grant funded a two day meeting at Northwestern University held on May 10-11, 2014. This was the 73rd in the series of Midwest Partial Differential Equations ("PDE") Seminars. The main focus of this meeting was on PDE's that arise in the context of geometry, interpreted very broadly. The meeting brought together several diverse communities working in geometric analysis of different kinds, and the mixture of techniques and goals on display in the talks provided a good cross-fertilization. The speakers and their talk titles were as follows: Semyon Dyatlov, "Pollicott-Ruelle resonances for hyperbolic manifolds"; Nicolas Burq, "Gibbs measures and weak solutions to some dispersive PDE's"; Fanghua Lin, "Large N asymptotics of optimal partitions of Dirichlet eigenvalues"; Yanyan Li, "Some analytic aspects of conformally invariant fully nonlinear equations"; Svitlana Mayboroda, "Localization of eigenfunctions and associated free boundary problems"; Lei Ni, "Entropy and Gauss curvature flow"; Aaron Naber, "The structure of metric-measure spaces with lower Ricci curvature bounds". There were more than 50 junior participants in the meeting, which provided the students and postdocs in attendance with a broad overview of current developments in several areas of PDE. Two different NSF grants (this and DMS-121654) supported the conference, along with the Northwestern University Mathematics department. The two NSF grants together funded 32 participants in the conference in addition to the speakers.
