Principal Investigator: Jeremy Tyson, Luca Capogna and Scott Pauls
The conference "Geometric Analysis and Applications" will take place at the University of Illinois at Urbana-Champaign in July 2006. The focus of the conference will be on recent developments in the study of analysis and geometry in metric measure spaces with a particular emphasis on geometric analysis, geometric measure theory and subelliptic PDE in Carnot groups and general sub-Riemannian manifolds. Applications of these subjects to problems in robotics, control theory, the geometry of the visual cortex, and digital image reconstruction will also receive significant attention. An important aim of the conference is to provide a forum for the exchange of ideas among researchers in a variety of pure and applied fields and to foster new avenues for collaboration and exchange.
The basic theme of sub-Riemannian geometry is the "geometry of constrained motion"; it provides mathematical models for any physical situation in which allowable motion is subject to specific a priori geometric constraints. Historically, the roots of the subject lie in Carnot's work on thermodynamics and adiabatic processes, but it has progressed significantly beyond these motivating questions to a central position in modern nonsmooth geometric analysis, and has seen remarkable applications in numerous areas: robotic path planning, remote control of satellites and unmanned aerial vehicles, digital image reconstruction and computer vision, neurobiology, and the mathematics of finance, to name a few. The goal of the conference is to bring together a wide spectrum of pure and applied mathematicians with common interests in the subject of sub-Riemannian geometry to develop new methods and techniques for its study. Special emphasis will be placed on supporting graduate students and junior participants, to train the next generation of researchers in this exciting and rapidly expanding field and to lay the foundation for a "North American" school in this area on a par with the established centers of research in sub-Riemannian and Carnot-Caratheodory geometry in Europe. Further information regarding the conference can be found at www.math.uiuc.edu/~tyson/UIUC06.html
