Workshop on Analysis and Geometry in Several Complex Variables

一个题为"分析和几何在几个复杂的变量"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。&本次研讨会将汇集来自海湾地区，巴西，美国和欧洲的领先研究人员，年轻的博士后和研究生。已为本次研讨会建立了网站：www.example.com。研讨会的目的有两个。第一，促进不同地区数学家之间的长期合作。第二，为年轻的参与者提供与所在领域的领导者互动的机会，以及相互之间的互动。该主题，几个复杂的变量，享有中心地位，在数学，因为它提请，并有助于，各种其他子领域的数学。但是，虽然它在数学本身中有充分的动机，但它也出现在各种其他背景中。例如，因果关系，自然的基本定律之一，当通过称为傅立叶变换的数学装置转录时，立即导致几个虽然Cauchy-Riemann方程的Sobolev理论发展得很好，但CR子流形上的类似物的理论，切向Cauchy-Riemann方程，是在一个可比的阶段，只为子流形的超曲面型。但即使在这些情况下，关于紧性、全局正则性等基本问题，保持开放。很明显，为了解决这些问题，并将理论扩展到非超曲面型的CR子流形，现代CR几何的技术将是至关重要的。CR函数和CR映射自然地从切向柯西-黎曼算子中产生，分别作为核中的函数和作为关于CR结构（基本对象）的映射。在这一非常活跃的研究领域中，一些经典问题仍然悬而未决。拟议的讲习班将这些领域的专家聚集在一起，旨在开展合作，从而在这些问题上取得实质性进展。此外，关于复杂的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。

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.