The University of North Carolina (UNC) Department of Mathematics plans to host a week long conference entitled "A Conference on Partial Differential Equations - Analytic and Geometric Aspects" in Chapel Hill from July 16-20, 2012 relating to microlocal analysis and geometry in partial differential equations (PDE). This conference will bring together experts in the fields of microlocal and geometric analysis, which dramatically impact the study of partial differential equations, geometry, topology and spectral theory. Though such fields rarely interact in focused conferences, they often have an overlap of useful techniques and ideas that would allow for collaborations to make advancements in both analysis and geometry. In particular, the conference would bring together many experts whose insights into geodesic flow and geometry could dramatically inform and advance the University of North Carolina analysis group's efforts to understand the existence and dynamics of nonlinear bound states on manifolds, which have arisen in the studies of both geometry and dispersive equations.
This project supports participation in the conference on Partial Differential Equations - Analytic and Geometric Aspects. Funds will be used for the travel and housing costs for speakers, graduate students, postdocs and junior faculty at U.S. universities without NSF support who would like to participate in the conference. This workshop will reflect the main areas of focus of the partial differential equations group at the University of North Carolina, which has grown around distinguished senior faculty member Michael Taylor, who has made fundamental contributions to PDE throughout his career, in particular helping to develop the topics of microlocal and geometric analysis in the study thereof. The group has wishes to bring in experts and students from around the world to discuss recent advances, in particular related to nonlinear partial differential equations on manifolds and applications. Such techniques have led to a surge in activity touching such areas as general relativity, fluid mechanics, and nonlinear optics. More details for the conference can be found at
www.math.psu.edu/mazzucat/uncconf2012/index.html
This continuing grant funded three mini-schools in Partial Differential Equations throughout the academic year of 2013-2014 at the University of North Carolina, Chapel Hill. The first lecture was by Kevin Zumbrun of Indiana University, who spoke about the stability of periodic solutions in models related to water waves. The second lecture was by Christopher Sogge of Johns Hopkins University on eigenfunctions of the Laplacian on compact manifolds without boundary. The third was by Maciej Zworski who spoke on dynamical zeta functions and introducing the subject of microlocal analysis. In fact, microlocal anaylsis was a central theme in all three talks, which is a key topic for analyzing problems that have a fixed energy. In the end, the goal of all these projects is to understand better the solutions to problems from dispersive partial differential equations. This is an area that uses harmonic analytic tools for describing problems from physics in areas as diverse as quantum mechanics to fluid flows. In addition to introducing graduate students to major topics of modern research in a setting where they have access to the experts, the Mini-Schools posted online all the lecture notes and featured talks by more advanced graduate students who had a chance to disseminate their results and talk to their peers about future directions.
