Workshop on Analysis and Geometry in Several Complex Variables
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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.
