Conference series in geometric analysis and sub-Riemannian geometry

项目负责人：Jeremy Tyson、Luca Capogna和Scott pauls“几何分析与应用”会议将于2006年7月在伊利诺伊大学香槟分校举行。会议的重点将是度量空间中分析和几何研究的最新进展，特别强调几何分析、几何测量理论和卡诺群和广义亚黎曼流形中的亚椭圆偏微分方程。这些学科在机器人、控制理论、视觉皮质几何和数字图像重建等问题上的应用也将受到极大的关注。会议的一个重要目的是为各种纯领域和应用领域的研究人员提供一个交流思想的论坛，并促进合作和交流的新途径。亚黎曼几何的基本主题是“受限运动几何”；它为任何物理情况提供了数学模型，其中允许的运动受到特定的先验几何约束。从历史上看，这门学科的根源在于卡诺对热力学和绝热过程的研究，但它已经大大超越了这些激励问题，在现代非光滑几何分析中占据了中心地位，并在许多领域得到了显著的应用：机器人路径规划、卫星和无人机的远程控制、数字图像构建和计算机视觉、神经生物学和金融数学，等等。会议的目标是将广泛的对亚黎曼几何有共同兴趣的纯粹和应用数学家聚集在一起，为其研究开发新的方法和技术。特别强调的是支持研究生和初级参与者，在这个令人兴奋和迅速发展的领域培养下一代研究人员，并为该领域的“北美”学校奠定基础，与欧洲建立的亚黎曼几何和卡诺-卡拉几何研究中心齐名。有关会议的更多信息可在www.math.uiuc.edu/~tyson/UIUC06.html上找到

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