Workshop on Analysis and Geometry in Several Complex Variables

多个复杂变量的分析与几何研讨会

• 批准号: 1500361
• 负责人: Emil Straube
• 金额: $ 4.84万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-12-01 至 2015-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1500361&HistoricalAwards=false
• 关键词: Workshop; Analysis; Geometry; Several; Complex

A workshop titled "Analysis and Geometry in Several Complex Variables" will be held at Texas A&M University Qatar in Doha, Qatar, January 4-8, 2015. This workshop will bring together leading researchers, young post-docs, and graduate students from the Gulf region, Brazil, the US, and Europe. A website has been set up for this workshop at http://science.qatar.tamu.edu/Conferences/Pages/Upcoming-Conferences.aspx. The purpose of the workshop is twofold. First, to generate long term collaborations between mathematicians from the different regions. Second, to afford the younger participants an opportunity to interact with leaders in their field, as well as with each other. The subject matter, several complex variables, enjoys a central position in mathematics because it draws from, and contributes to, various other subareas of mathematics. But while it is amply motivated within mathematics proper, it also arises in various other contexts. For example, causality, one of the fundamental laws of nature, when transcribed via a mathematical device called Fourier transform, immediately leads to analytic functions of several (in this case four) complex variables.While the Sobolev theory of the Cauchy-Riemann equation(s) is well developed, the theory for the analogue on CR submanifolds, the tangential Cauchy-Riemann equation(s), is at a comparable stage only for submanifolds of hypersurface type. But even in these cases, fundamental questions concerning compactness, global regularity, etc., remain open. It has become clear that in order to address these questions, and to extend the theory to CR submanifolds that are not of hypersurface type, techniques of modern CR geometry will be crucial. CR functions and CR mappings arise naturally form the tangential Cauchy-Riemann operator, as functions in the kernel and as mappings that respect the CR structures (the basic object), respectively. A number of classical questions remain open in this very active area of research as well. By bringing together experts from these areas, the proposed workshop aims to initiate collaborations that will lead to substantial progress on these issues. In addition, a short course on complex Brunn-Minkowski theory will provide an introduction to an exciting new perspective on some of the "classical" techniques.

题为“多个复杂变量的分析和几何”的研讨会将于 2015 年 1 月 4 日至 8 日在卡塔尔多哈的德克萨斯 A&M 大学卡塔尔分校举行。该研讨会将汇集来自海湾地区、巴西、美国和欧洲的顶尖研究人员、年轻博士后和研究生。本次研讨会已建立一个网站：http://science.qatar.tamu.edu/Conferences/Pages/Upcoming-Conferences.aspx。研讨会的目的是双重的。首先，在不同地区的数学家之间建立长期合作。其次，为年轻参与者提供与各自领域的领导者以及彼此之间互动的机会。这个主题，即几个复杂的变量，在数学中享有中心地位，因为它借鉴并贡献于数学的各个其他子领域。尽管它在数学本身中有充分的动机，但它也在其他各种背景下出现。例如，因果关系是自然的基本定律之一，当通过称为傅里叶变换的数学装置转录时，立即导致几个（在本例中为四个）复变量的解析函数。虽然柯西-黎曼方程的索博列夫理论已经得到很好的发展，但 CR 子流形的类似理论，即切向柯西-黎曼方程，仅处于可比较的阶段 超曲面类型的子流形。但即使在这些情况下，有关紧致性、全局规律性等基本问题仍然悬而未决。很明显，为了解决这些问题，并将理论扩展到非超曲面类型的 CR 子流形，现代 CR 几何技术将至关重要。 CR 函数和 CR 映射自然地从切向柯西-黎曼算子产生，分别作为内核中的函数和尊重 CR 结构（基本对象）的映射。在这个非常活跃的研究领域中，许多经典问题仍然悬而未决。通过汇集这些领域的专家，拟议的研讨会旨在发起合作，从而在这些问题上取得实质性进展。此外，关于复杂 Brunn-Minkowski 理论的短期课程将介绍一些“经典”技术的令人兴奋的新视角。