Award: DMS 0509068, 0508661, 0509714 Principal Investigator: Thomas P. Branson, Shihshu Walter Wei, Andrzej J. Derdzinski Institutions: University of Iowa, University of Oklahoma, Ohio State University
The Midwest Geometry Conference has been meeting annually since 1991. Its goal is to present recent advances in differential geometry, geometric analysis, and integral geometry to geometers from the Midwest, including junior level researchers and some graduate students. The main part of the program consists of several plenary lectures given by experts in specific sub-fields (who need not be Midwest-based); an opportunity is also provided for some of the participants to give contributed talks. The current project provides for conferences in the spring of 2005, 2006, and 2007 at the Ohio State University, the University of Oklahoma and, respectively, the University of Iowa. The Ohio State conference, planned for April 29 to May 1, 2005, will focus on three topics: positively curved manifolds; Ricci flow, solitons and Einstein metrics; geometric group theory. The lists of topics for the other two conferences are still tentative, and include: symmetric criticality; p-harmonic geometry; convexity, positively curved manifolds, and Ricci flow (Oklahoma, 2006), as well as: symmetries and overdetermined systems of PDEs; the AdS/CFT correspondence; nonlinear hyperbolic evolution equations; geometric scattering theory (Iowa, 2007).
The Midwest Geometry Conference is dedicated to the exchange of ideas among members of the geometry community in the Midwest, as well as dissemination of important research advances and ideas, nationwide and worldwide, in differential geometry and related fields. A key objective of the conference is the attempt to encourage researchers and potential researchers in the Midwest, especially those who work some distance from the large research centers, as well as young people, women, and members of underrepresented groups. "Warm-up" sessions for graduate students and young researchers are planned for the days leading up to the conference. At least one of the three or four focus topics at each conference is related to applications of geometry. Historically, such applications lie primarily in physics, with prominent examples provided by Einstein's general theory of relativity and the currently accepted Standard Model of elementary particles and their interactions. Other well-known applications of differential geometry are in engineering, for example robotics. A further example pertains to evolution equations, which are currently a subject of keen interest to differential geometers and, at the same time, have the applied aspect of describing how some materials, or the space itself, develop in time. A very specific example of the latter kind is provided by the mean curvature flow. The surface of a globule of molten plastic evolves, or adapts in time, to have the minimum possible curvature; this evolution is completely determined by the globule's curvature. This fundamental observation provides an understanding of a wide range of flow problems, and allows an approach to predicting the flow. This has immediate relevance to injection molding of materials, for example in the dashboards and bumpers of automobiles. But the fundamental principles behind mean curvature flow have also provided a paradigm for problems like the Ricci flow, in which the metric properties of space itself are the quantities which are evolving. Questions of the latter kind will be central to the coming meetings of the Midwest Geometry Conference.
