Informal seminar on combinatorics and representation theory

This is an informal seminar on combinatorics and representation theory. In Fall 2020 we plan to focus on the recent work of Blasiak, Morse and Pun on Catalan polynomials.
Organizers: Erik Carlsson , Eugene Gorsky, Anne Schilling, Monica Vazirani .
The seminar meets on Mondays at 2-3pm.
Notes from other quarters: Winter 21 .

Program

• 10/5 Anne: introduction to k-Schur functions and Catalan polynomials notes
• 10/12 Eugene: Catalan functions and Hall-Littlewood polynomials [BMPS2,Section 4] notes
• 10/19 Monica: Recurrences for Catalan functions [BMPS2,Section 5] notes
• 10/26 Daniel: Catalan functions and k-Schur functions [BMPS2,Section 2] notes
• 11/2 Wencin: Nonsymmetric Catalan functions, recursions, operator formula [BMP, Section 5, Theorem 2.3] notes
• 11/9 Wencin continues notes
• 11/16 Nicolle: Demazure crystals [BMP, Section 4] notes
• 11/23 Nicolle continues notes
• 11/30 and 12/7 Jianping: DARK crystals [BMP, Section 6] notes
• Winter break
• Seminar continues in Winter quarter here

References:

1. [BMP] Jonah Blasiak, Jennifer Morse, Anna Pun. Demazure crystals and the Schur positivity of Catalan functions. arXiv:2007.04952
2. [BMPS1] Jonah Blasiak, Jennifer Morse, Anna Pun, Daniel Summers. k-Schur expansions of Catalan functions. arXiv:1811.02490
3. [BMPS2] Jonah Blasiak, Jennifer Morse, Anna Pun, Daniel Summers. Catalan functions and k-Schur positivity. arXiv:1804.03701
4. [Katalan] Jonah Blasiak, Jennifer Morse, George Seelinger. K-theoretic Catalan functions. arXiv:2010.01759