Informal seminar on combinatorics and representation theory

[THIS WEBPAGE IS ARCHIVED]

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