Conference series in geometric analysis and sub-Riemannian geometry

点击翻译按钮获取中文摘要

AbstractAward: DMS-0548644Principal Investigator: Jeremy Tyson, Luca Capogna and Scott PaulsThe conference "Geometric Analysis and Applications" will takeplace at the University of Illinois at Urbana-Champaign in July2006. The focus of the conference will be on recent developmentsin the study of analysis and geometry in metric measure spaceswith a particular emphasis on geometric analysis, geometricmeasure theory and subelliptic PDE in Carnot groups and generalsub-Riemannian manifolds. Applications of these subjects toproblems in robotics, control theory, the geometry of the visualcortex, and digital image reconstruction will also receivesignificant attention. An important aim of the conference is toprovide a forum for the exchange of ideas among researchers in avariety of pure and applied fields and to foster new avenues forcollaboration and exchange.The basic theme of sub-Riemannian geometry is the "geometry ofconstrained motion"; it provides mathematical models for anyphysical situation in which allowable motion is subject tospecific a priori geometric constraints. Historically, the rootsof the subject lie in Carnot's work on thermodynamics andadiabatic processes, but it has progressed significantly beyondthese motivating questions to a central position in modernnonsmooth geometric analysis, and has seen remarkableapplications in numerous areas: robotic path planning, remotecontrol of satellites and unmanned aerial vehicles, digital imagereconstruction and computer vision, neurobiology, and themathematics of finance, to name a few. The goal of the conferenceis to bring together a wide spectrum of pure and appliedmathematicians with common interests in the subject ofsub-Riemannian geometry to develop new methods and techniques forits study. Special emphasis will be placed on supporting graduatestudents and junior participants, to train the next generation ofresearchers in this exciting and rapidly expanding field and tolay the foundation for a "North American" school in this area ona par with the established centers of research in sub-Riemannianand Carnot-Caratheodory geometry in Europe. Further informationregarding the conference can be found atwww.math.uiuc.edu/~tyson/UIUC06.html