Geometric Analysis -- A Conference in Luminy, France, Winter 2011

几何分析——2011 年冬季在法国 Luminy 举行的会议

• 批准号: 1062288
• 负责人: Andras Vasy
• 金额: $ 1.06万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-12-01 至 2011-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1062288&HistoricalAwards=false
• 关键词: Geometric; Analysis; Conference; Luminy; France

On January 17-21, 2011, there will be a one-week conference at Luminy, France on recent advances in geometric analysis, with the title `Geometric Analysis'. Within the general field of geometric analysis, the conference will focus on microlocal analysis, spectral geometry, conformal invariants, analysis on non-compact manifolds including the study of index theory and de Rham cohomologies as well as wave propagation, and the study of geometric flows. These topics are chosen because of many recent advances and numerous open frontiers, and because in spite of many connections between them, there is sufficient distance between these topics that collaborative projects, benefitting from different points of view, are particularly fruitful. In particular, the conference is expected to facilitate productive interactions between researchers working on elliptic and parabolic (which are the traditional strengths of the field), respectively hyperbolic (such as wave propagation), problems in partial differential equations. The proposal serves to provide for the transportation to the conference, and accomodation there, for some participants, with emphasis on graduate students, postdoctoral fellows, and junior faculty from US universities.Geometric analysis covers areas in which one studies phenomena, such as wave propagation or heat flow, on geometric backgrounds. One example of such a geometric background is general relativity, giving rise to a curved space-time of great physical interest. It also gives rise to `static' problems, without a `time' variable; the latter have received much of the attention as they are analytically more tractable. While often there is a physical motivation, recent work in the Ricci flow, which is an analogue of heat flow, shows that the field can also be used to answer questions of mathematical origin, in this case in topology (the study of shapes). This conference combines both aspects, and strives to encourage collaboration between researchers in different areas. It is also designed be ideal for doctoral students and young researchers as it will provide them with a host of techniques and problems relevant to their research. In particular, the speakers will be asked that the talks explain both the methods used and the motivations for the problem be it from a pure or an applied perspective, and there will be a discussion of new and open problems as well; this is expected to help young researchers just starting work in the field.

2011年1月17日至21日，将在法国Luminy举行为期一周的会议，讨论几何分析的最新进展，题目是“几何分析”。在几何分析的一般领域内，会议将侧重于微局部分析，谱几何，共形不变量，对非紧流形的分析，包括指数理论和德拉姆上同调以及波传播的研究，以及几何流动的研究。选择这些主题是因为许多最新的进展和许多开放的前沿，因为尽管它们之间有许多联系，但这些主题之间有足够的距离，从不同的观点受益的合作项目特别富有成效。特别是，会议预计将促进研究人员之间的富有成效的互动椭圆和抛物线（这是该领域的传统优势），分别双曲（如波传播），偏微分方程的问题。该提案旨在为一些与会者提供会议的交通和住宿，重点是研究生，博士后研究员和美国大学的初级教师。几何分析涵盖了人们研究现象的领域，如波传播或热流，几何背景。这种几何背景的一个例子是广义相对论，它产生了一个具有巨大物理意义的弯曲时空。它还引起了“静态”问题，没有一个“时间”变量;后者受到了很大的关注，因为它们在分析上更容易处理。虽然经常有一个物理的动机，最近的工作在里奇流，这是一个类似的热流，表明该领域也可以用来回答问题的数学起源，在这种情况下，在拓扑学（形状的研究）。这次会议结合了这两个方面，并努力鼓励不同领域的研究人员之间的合作。它也被设计为博士生和年轻的研究人员的理想选择，因为它将为他们提供一系列与他们的研究相关的技术和问题。特别是，演讲者将被要求从纯粹或应用的角度解释所使用的方法和问题的动机，并将讨论新的和开放的问题;这有望帮助年轻的研究人员刚刚开始在该领域的工作。