Collaborative Research: Midwest Geometry Conference 2005-2007

合作研究：中西部几何会议 2005-2007

• 批准号: 0508661
• 负责人: Shihshu Walter Wei
• 金额: $ 1.2万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-04-15 至 2008-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0508661&HistoricalAwards=false
• 关键词: Collaborative; Research; Midwest; Geometry; Conference

AbstractAward: DMS 0509068, 0508661, 0509714Principal Investigator: Thomas P. Branson, Shihshu Walter Wei, Andrzej J. DerdzinskiInstitutions: University of Iowa, University of Oklahoma,Ohio State UniversityThe Midwest Geometry Conference has been meeting annually since1991. Its goal is to present recent advances in differentialgeometry, geometric analysis, and integral geometry to geometersfrom the Midwest, including junior level researchers and somegraduate students. The main part of the program consists ofseveral plenary lectures given by experts in specific sub-fields(who need not be Midwest-based); an opportunity is also providedfor some of the participants to give contributed talks. Thecurrent project provides for conferences in the spring of 2005,2006, and 2007 at the Ohio State University, the University ofOklahoma and, respectively, the University of Iowa. The OhioState conference, planned for April 29 to May 1, 2005, will focuson three topics: positively curved manifolds; Ricci flow,solitons and Einstein metrics; geometric group theory. The listsof topics for the other two conferences are still tentative, andinclude: symmetric criticality; p-harmonic geometry; convexity,positively curved manifolds, and Ricci flow (Oklahoma, 2006), aswell as: symmetries and overdetermined systems of PDEs; theAdS/CFT correspondence; nonlinear hyperbolic evolution equations;geometric scattering theory (Iowa, 2007).The Midwest Geometry Conference is dedicated to the exchange ofideas among members of the geometry community in the Midwest, aswell as dissemination of important research advances and ideas,nationwide and worldwide, in differential geometry and relatedfields. A key objective of the conference is the attempt toencourage researchers and potential researchers in the Midwest,especially those who work some distance from the large researchcenters, as well as young people, women, and members ofunderrepresented groups. "Warm-up" sessions for graduatestudents and young researchers are planned for the days leadingup to the conference. At least one of the three or four focustopics at each conference is related to applications of geometry.Historically, such applications lie primarily in physics, withprominent examples provided by Einstein's general theory ofrelativity and the currently accepted Standard Model ofelementary particles and their interactions. Other well-knownapplications of differential geometry are in engineering, forexample robotics. A further example pertains to evolutionequations, which are currently a subject of keen interest todifferential geometers and, at the same time, have the appliedaspect of describing how some materials, or the space itself,develop in time. A very specific example of the latter kind isprovided by the mean curvature flow. The surface of a globule ofmolten plastic evolves, or adapts in time, to have the minimumpossible curvature; this evolution is completely determined bythe globule's curvature. This fundamental observation providesan understanding of a wide range of flow problems, and allows anapproach to predicting the flow. This has immediate relevance toinjection molding of materials, for example in the dashboards andbumpers of automobiles. But the fundamental principles behindmean curvature flow have also provided a paradigm for problemslike the Ricci flow, in which the metric properties of spaceitself are the quantities which are evolving. Questions of thelatter kind will be central to the coming meetings of the MidwestGeometry Conference.

Abstractaward：DMS 0509068，0508661，0509714Principal调查员：Thomas P. Branson，Shihshu Walter Wei，Andrzej J. Derdzinskiinstitutions：爱荷华州俄克拉荷马大学，俄亥俄州俄亥俄州州立大学中部麦格尔大学的Midwest Geotormentry会议上已经召开了Midwest Geormementry会议。 它的目标是介绍从中西部的几何学，包括初级研究人员和一些毕业生的几何形状的差异测定学，几何分析和整体几何形状的最新进展。 该计划的主要部分是由专家在特定子场（不需要基于中西部）的专家进行的。还为一些参与者提供了机会进行演讲。 Thecurrent项目于2005年春季提供会议，并在2007年在俄亥俄州立大学，分别在爱荷华大学和爱荷华大学举行会议。 计划于4月29日至2005年5月1日举行的OhioState会议将重点关注三个主题：正面弯曲的歧管； Ricci流，孤子和爱因斯坦指标；几何群体理论。 其他两个会议的主题列表仍然是暂定的，包括：对称的批判性； p谐波几何形状；凸度，正面弯曲的歧管和Ricci流动（俄克拉荷马州，2006年），同样是：PDES的对称性和过度确定系统； theads/cft对应；非线性双曲进化方程；几何散射理论（爱荷华州，2007年）。中西部几何会议致力于中西部几何群落成员之间的交换，就像传播重要的研究进步和思想，全国和全球的重要研究进步，在不同的几何和全球范围内。 会议的关键目标是中西部的招聘研究人员和潜在的研究人员，尤其是那些与大型研究中心以及年轻人，妇女和法人表述群体成员一定距离的人。 计划在毕业生和年轻研究人员的“热身”课程中，以导致会议的日子。 每个会议中的三个或四个峰中的至少一个与几何学的应用有关。从历史上讲，这种应用主要在于物理学，并提供了爱因斯坦一般理论的余量理论和当前接受的标准的谈式式粒子及其相互作用的示例。 差异几何形状的其他众所周知的应用程序是工程，例如 另一个示例与进化方程有关，目前是一个敏锐的兴趣的主题，同时具有描述某些材料或空间本身如何及时发展的应用。 平均曲率流得到了一种非常具体的例子。 莫尔顿塑料的球的表面会随着最小的曲率而变化，或者及时适应。这种进化完全取决于球的曲率。 这种基本观察可以使人们对各种流动问题的了解，并允许预测流量。 这与材料的注入成型有关，例如在汽车的仪表板和轰动机中。 但是，曲率流的基本原理也为RICCI流动的问题提供了一个范式，其中空间自我的度量特性是正在发展的数量。 THELTEST类型的问题将是中西部阶层会议的即将到来的会议的核心。