Elliptic Orthogonal Polynomials and Their Integrability

Explore a 45-minute conference talk on elliptic orthogonal polynomials and their integrability presented by Harini Desiraju from the Sydney Mathematical Research Institute, University of Sydney. Delve into a generalized framework using Riemann-Hilbert analysis to study these special functions that satisfy orthogonality conditions with respect to a weight function on an elliptic curve. Discover how this approach leads to associated discrete and continuous integrable systems. Examine a demonstration of how the elliptic formulation of the sixth Painlevé equation can be recovered for the simplest weight function. Gain insights into advanced mathematical concepts presented at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop, recorded on May 23, 2024, at UCLA.