Lecture 1: The AAA algorithm for rational approximation
Monday October 6, 2025 at 16:00, SERC 110A
With the introduction of the AAA algorithm in 2018 (Nakatsukasa-Sete-T., SISC), the computation of rational approximations changed from a hard problem to an easy one. We've been exploring the implications of this transformation ever since. This talk will review the algorithm and then present demonstrations of applications in areas including interpolation of missing data, analytic continuation, function extension, analysis of solutions of dynamical systems, model order reduction, nonlinear eigenvalues, and numerical computation of the Schwarz function.
Lecture 2: From rational approximation to Helmholtz scattering
Tuesday October 7, 2025 at 10:00, Wachman 617
The new lightning and AAA rational approximation algorithms lead to new possibilities for numerical solution of certain PDEs in the plane. We present applications to Laplace, Stokes, and Helmholtz equations. We also discuss another application in Helmholtz scattering, independent of how the scattered fields are computed (e.g. by integral equations): the use of rational approximation to determine complex resonances for a nonconvex scatterer such as a "corral". This second part of the talk is joint work with Oscar Bruno and Manuel Santana at Caltech.
Lecture 3: Fifteen images for discussion
Tuesday October 7, 2025 at 14:00, Wachman 617
What does it mean to be a scientist, a mathematician, a numerical mathematician in 2025? This event will be a reflection on such questions based on fifteen images from my intellectual life past and present. Everybody is welcome and I look forward to a two-way conversation.
