CBMS Conference: The Solution of Problems in Multiply-Connected Domains

该国家科学基金会奖支持2018年6月18日至22日在加州大学欧文分校举行的为期5天的CBMS会议，主题是“多重连接域中的问题的解决方案”。总的来说，这次会议的基础是使用复杂分析的方法来解决水波、流体流动和核物理中出现的问题。会议的主要演讲人是伦敦帝国理工学院的达伦·克劳迪教授。他是复杂分析应用方面的顶尖专家。克劳迪教授将发表10场讲座，并出版一部将在CBMS系列上发表的专著，为数学家和工程师提供重要的参考。该奖项将赞助来自南加州和美国其他地区的不同的演讲者和与会者。选定的日期是在SIAM关于非线性波和相干结构的会议之后，该会议将于2018年6月11日至14日在附近的加利福尼亚州阿纳海姆举行。这项活动增加了南加州的研究活动。复杂分析中的高级主题正在从计算的角度进行研究，并增加了深度。重要的例子有共形映射的数值计算，用各种方法计算紧黎曼曲面和黎曼-希尔伯特问题的数值解。这些主题对于大量的(应用)数学领域是重要的，例如可积偏微分方程、随机矩阵理论、特殊函数等。这些主题本身导致了各种科学和工程应用。最近，在多相物理中，已经认识到所谓的拉普拉斯增长问题具有潜在的可积结构，将其与Toda和Whitham可积族联系起来。在过去20年中，主要发言者在很大程度上参与了这些事态发展。克劳迪教授开创了一种解决多连通平面区域问题的新的建设性框架，在应用科学中产生了一系列新的结果。克劳迪教授工作的一个最明显的例子是他从1860年起将著名的Schwarz-Christoffel公式推广到多连通区域。会议网址为：https://www.math.uci.edu/~ttrogdon/ACCA.html

This National Science Foundation award supports a 5-day CBMS conference on "The Solution of Problems in Multiply-Connected Domains," at the University of California Irvine, Irvine, CA, June 18-22, 2018. Broadly, this conference is based around the use of methods from complex analysis to solve problems that arise in water waves, fluid flow and nuclear physics. The conference features the principal speaker, Professor Darren Crowdy of Imperial College London. He is a leading expert on the applications of complex analysis. Prof. Crowdy will deliver 10 lectures and produce a monograph to be published in the CBMS series, providing an important reference for mathematicians and engineers. This award will sponsor a diverse group of additional speakers and attendees from both Southern California and the the remainder of the United States. The chosen dates follow the SIAM meeting on Nonlinear Waves and Coherent Structures which will be held in nearby Anaheim, CA, June 11-14, 2018. This activity increases the research activity within Southern California.Advanced topics in complex analysis are being studied from a computational point of view with increased depth. Important examples are the numerical computation of conformal mappings, computing with compact Riemann surfaces using a variety of methods and the numerical solution of Riemann-Hilbert problems. These topics are important for a large array of (applied) mathematical areas such as integrable partial differential equations, random matrix theory, special functions, etc. These themselves lead to a variety of science and engineering applications. Very recently, in multi-phase physics the so-called Laplacian growth problem has been realized to have an underlying integrable structure linking it to the Toda and Whitham integrable hierarchies. The principal speaker has been very much a part of these developments in the last 20 years. Prof. Crowdy has pioneered a new constructive framework for solving problems in multiply connected planar domains which has led to a panoply of new results in the applied sciences. One of the most visible examples of Prof. Crowdy's work is his extension of the famous Schwarz-Christoffel formula from 1860 to multiply connected domains. The conference website is located at: https://www.math.uci.edu/~ttrogdon/ACCA.html