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An invitation to "classic" multiple orthogonal polynomials

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AR2W03 - Applicable resurgent asymptotics: summary workshop

The realm of applications of orthogonal polynomials (OP) in mathematics, physics, engineering, computer science is widely acknowledged. Partly because they sit at the intersection of analysis, numerical analysis, approximation theory, spectral theory, special functions, number theory, combinatorics, mathematical physics, among others. Multiple orthogonal polynomials (MOP) are an extension of OP. Essentially, they consist of a set of polynomials in a single variable satisfying orthogonality conditions with respect to a vector of measures. They arose in the context of number theory and nowadays they are tools in studies in rational approximation, random matrices, number theory, integrable systems, geometric function theory. Their development was motivated by their appearance of new applications, where OPs were not the best tools in addressing the challenge. In the meantime, several new families of multiple orthogonal polynomials have been studied, widely extending the collection of the well known classical orthogonal polynomials, and adding new special functions.  In this talk I will explain the main features and charms of multiple orthogonality. The focus will be on MOP with respect a vector of measures expressed in terms of hypergeometric functions, highlighting their connections to combinatorics, integrable systems, spectral theory and random matrices. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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