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，法国Luminy将在几何分析的最新进展中举行一周的会议，标题为“几何分析”。在几何分析的一般领域中，会议将集中于微局部分析，光谱几何形状，保形不变式，对非紧密歧管的分析，包括研究指数理论和DE RHAM共同体的研究以及波传播以及几何流量的研究。之所以选择这些主题，是因为最近的许多进步和许多开放的前沿，而且由于它们之间有许多联系，这些主题之间仍有足够的距离，使得协作项目从不同的角度受益，这尤其富有成果。特别是，该会议有望促进从事椭圆形和抛物线派（这是该领域的传统优势）的研究人员之间的生产性相互作用，分别是双曲线（例如波浪传播），部分区分方程中的问题。该提案旨在为某些参与者提供到会议的运输，并为某些参与者提供住宿，重点是研究生，博士后研究员和来自美国大学的初级教师。几何分析涵盖了一种研究领域，其中一种研究现象，例如波浪传播或热流量，几何背景。这种几何背景的一个例子是总体相对论，引起了极大的身体兴趣的弯曲时空。它也引起了“静态”问题，没有“时间”变量；后者在分析上更容易拖延，因此受到了很多关注。尽管经常有身体动机，但在RICCI流中的最新工作是热流的类似物，表明该领域也可以用于回答数学起源的问题，在这种情况下，在拓扑结构中（形状研究）。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。它的设计也是博士学生和年轻研究人员的理想选择，因为它将为他们提供与研究相关的许多技术和问题。特别是，将询问演讲者的谈话可以解释所使用的方法和问题的动机，包括从纯粹的角度看，也将讨论新的和开放的问题。预计这将帮助年轻的研究人员刚刚开始在该领域的工作。