Title : Introduction to Macdonald polynomials

Speaker : Dr. Jaeseong Oh (KIAS)

Abstract : Macdonald polynomials form a distinguished basis for the ring of symmetric functions, with profound connections to combinatorics, geometry, representation theory, and probability. Over the past few decades, significant attention has been directed towards eigenoperators for Macdonald polynomials, such as the ∇ operator and the action of the elliptic Hall algebra on symmetric functions. These developments have led to the celebrated (n+1)n−1 theorem and the famous Shuffle Theorem, rich with elegant geometry and combinatorics, and have also uncovered fascinating links to knot homologies. In this lecture series, I will try to cover the following topics: