Recorded 23 May 2024. Harini Desiraju of the Sydney Mathematical Research Institute, University of Sydney, presents "Elliptic orthogonal polynomials and their integrability" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop. Abstract: Elliptic orthogonal polynomials are a family of special functions that satisfy certain orthogonality condition with respect to a weight function on an elliptic curve. I will present a generalized framework using Riemann-Hilbert analysis to study such polynomials and obtain associated discrete and continuous integrable systems. As a quick check, for the simplest weight function, I will show that the elliptic formulation of the sixth Painlevé equation can be recovered. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iv-vertex-models-algebraic-and-probabilistic-aspects-of-universality/