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

University Of California-Irvine, Irvine CA

Investigators

Abstract

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