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

2011年1月17日至21日，将在法国鲁米尼举行一次为期一周的会议，主题为‘几何分析’，讨论几何分析的最新进展。在几何分析的一般领域，会议将集中在微局部分析，谱几何，共形不变量，非紧流形上的分析，包括指数理论和De Rham上同调以及波传播的研究，以及几何流的研究。之所以选择这些主题，是因为最近取得的许多进展和许多开放的前沿，而且尽管它们之间有许多联系，但这些主题之间有足够的距离，因此受益于不同观点的合作项目特别富有成果。特别是，会议有望促进研究椭圆和抛物线(这是该领域的传统优势)的研究人员之间的富有成效的互动，分别研究偏微分方程组中的双曲型(如波传播)问题。该提案旨在为一些与会者提供前往会议的交通和住宿，重点是来自美国大学的研究生、博士后研究员和初级教师。几何分析涵盖了人们在几何背景下研究波传播或热流等现象的领域。这种几何背景的一个例子是广义相对论，它产生了一个极具物理意义的弯曲时空。它还会产生没有“时间”变量的“静态”问题；后者受到了很大的关注，因为它们在分析上更容易处理。虽然通常有物理动机，但最近在类似热流的Ricci流中的研究表明，场也可以用来回答数学起源的问题，在这种情况下，是在拓扑学(形状研究)中。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。它也是博士生和年轻研究人员的理想选择，因为它将为他们提供与他们的研究相关的一系列技术和问题。特别是，将要求发言者解释所使用的方法和解决问题的动机，无论是从纯粹的还是从应用的角度，还将讨论新的和开放的问题；这有望帮助刚刚开始这一领域工作的年轻研究人员。

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.