Mathematical Sciences DepartmentHarold J Gay Lecture SeriesFriday, September 12th, 20252:00PM at Stratton Hall 201Prof. Nick TrefethenProfessor of Applied Mathematics in Residence, Harvard UniversityThe AAA ALGORITHM FOR RATIONAL APPROXIMATION: 15 DEMOS AND 1 THEOREMWith the introduction of the AAA algorithm in 2018 (Nakatsukasa-Sète-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, computation of resonances, solution of Laplace problems, and conformal mapping. Then we will discuss and illustrate a theorem that explains so much about rational approximation, involving a Hermite contour integral in the complex plane.