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

CBMS会议：多连通域问题的解决方案

• 批准号: 1743920
• 负责人: Thomas Trogdon
• 金额: $ 3.5万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-11-01 至 2018-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1743920&HistoricalAwards=false
• 关键词: CBMS; Conference; Solution; Problems; Multiply

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

这项国家科学基金会奖在2018年6月18日至22日在加利福尼亚州欧文分校的加利福尼亚大学欧文分校举行了为期5天的CBMS会议，该会议是关于“多元连接领域中问题的解决方案”。该会议广泛地基于复杂分析的方法来解决水波，流体流动和核流动和核物理学中出现的问题。该会议的特色是主要发言人，伦敦帝国学院的Darren Crowdy教授。 他是复杂分析应用领域的领先专家。 Crowdy教授将提供10次讲座，并制作一篇专着，将在CBMS系列中发表，为数学家和工程师提供重要参考。该奖项将赞助来自南加州和美国其余部分的其他演讲者和与会者。选择的日期是在2018年6月11日至14日在加利福尼亚州附近举行的非线性波和连贯结构的SIAM会议之后。这项活动增加了南加州内部的研究活动。从计算中，正在研究复杂分析中的加入主题，以增加深度的观点。重要的例子是使用多种方法和riemann-hilbert问题的数值解决方案进行保形映射的数值计算，与紧凑的Riemann表面进行计算。这些主题对于大量（应用的）数学领域（例如可集成的部分微分方程，随机矩阵理论，特殊功能等）很重要。这些本身会导致各种科学和工程应用。最近，在多相物理学中，所谓的拉普拉斯生长问题已意识到具有基本的可集成结构，将其与TODA和WHITHAM可集成的层次结构联系起来。在过去的20年中，主要发言人一直是这些发展的一部分。 Crowdy教授开创了一个新的建设性框架，用于解决多重连接的平面域中的问题，从而导致了应用科学的新结果。 Crowdy教授作品的最明显的例子之一是他从1860年开始延伸到著名的Schwarz-Christoffel公式到乘以连接的领域。会议网站位于：https：//www.math.uci.edu/~ttrogdon/acca.html