POSTECH Representation Theory Seminar

General Information: This is a webpage where I keep track of events (sporadically) organized at POSTECH that can roughly be categorified as representation theory (to be understood in the broad, Gelfand sense, to include number theory, geometry, algebraic combinatorics etc.).

Events in the POSTECH-PMI Number Theory Seminar will not be cross-listed here.

Organizer: Valentin Buciumas

Lecture Series on Macdonald polynomials

Co-organized with Kyoung-Seog Lee . There will be two lectures on October 22 and October 24. Each lecture will be 2-2.5h long.

Date Time Speaker Affiliation Title Room
October 22, October 24 3:00pm-5:30pm Jaeseong Oh Korean Institute for Advanced Study Introduction to Macdonald polynomials Math Building Room 213
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 $\nabla$ 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:
  1. Fundamentals of symmetric functions
  2. The Macdonald polynomials
  3. The Shuffle Theorem and the Science Fiction Conjecture
  4. The elliptic Hall algebra and Khovanov-Rozansky homology of knots