Introduction to Science Fiction and q,t Catalan Numbers
Time: 2024-07-31
Published By: Wenqiong Li
Speaker(s): Jaeseong Oh (Korea Institute For Advanced Study)
Time: 10:00-11:00 August 16, 2024
Venue: Room 77201, Jingchunyuan 78, BICMR
Macdonald polynomials form an important family of symmetric functions due to their connections to representation theory, geometry, probability theory, and combinatorics. To study these polynomials, Bergeron and Garsia introduced the Science Fiction conjecture. In this talk, I will introduce Macdonald intersection polynomials that arise in the context of the Science Fiction conjecture and explore their relation to q,t Catalan numbers. If time permits, I will also present new discoveries on extending the Science Fiction conjecture and a new proof of the Loehr-Warrington conjecture. Based on joint works with Seung Jin Lee and Donghyun Kim.
