KU Combinatorics Seminar
Spring 2024

Friday 1/19
Organizational meeting

Friday 1/26
Jeremy Martin
Chromatic symmetric functions I: Basics and Crew's conjecture

Friday 2/2
Jeremy Martin
Chromatic symmetric functions II: Equivalence of the subtree and half-generalized degree polynomials

Abstract: Stanley introduced chromatic symmetric functions of graphs in a seminal 1995 paper and asked whether it is possible for two non-isomorphc trees to have equal CSFs. This problem remains open today and is considered very hard. I will discuss my recent work on deriving other graph invariants from the CSF, including Logan Crew's conjecture that the CSF of a tree determines its generalized degree sequence. (Don't worry, I will say what all these things mean and will not assume any prior knowledge about the CSF!) This is joint work with José Aliste-Prieto, Jennifer Wagner, and José Zamora.

Friday 2/9
Marge Bayer
Using discrete Morse theory for matching complexes

Friday 2/16
Reuven Hodges
Approximate Counting in Algebraic Combinatorics

Friday 2/23
No seminar

Friday 3/1
Jeremy Martin
The kernel of the chromatic symmetric function

Abstract: Stanley's problem about chromatic symmetric functions of trees can be reformulated linear-algebraically: does the kernel of the CSF, regarded as a linear transformation \(X\) from trees to symmetric functions, contain the difference of two trees in its kernel? The reformulation suggests trying to understand the kernel of \(X\). For general graphs, the map \(X\) is onto, and its kernel is generated by the modular relations of Guay-Paquet and Orellana-Scott, and for forests it is generated by the deletion/near-contraction relations of Aliste-Prieto, de Mier, Orellana and Zamora. For trees, \(X\) is not onto. We find the dimension of the cokernel of \(X\) (it's something nice) and have a partial description of a generating set for the kernel. This is joint work with José Aliste-Prieto, Jennifer Wagner, and José Zamora.

Friday 3/8
Shiliang Gao (U. Illinois, Urbana-Champaign)
Degrees of the stretched Kostka quasi-polynomials
Zoom coordinates: Meeting ID 995 1980 5587 (passcode 2024)

Abstract: The Kostka coefficient \(K_{\lambda,\mu}\) is the dimension of the weight space \(V^\lambda(\mu)\) in the irreducible representation \(V^\lambda\) of a complex semisimple Lie algebra. We provide a type-uniform formula for the degrees of the stretched Kostka quasi-polynomials \(K_{\lambda,\mu}(N):= K_{N\lambda,N\mu}\) in all classical types, improving and extending a previous result by McAllister in type A. Our proof relies on a combinatorial model for the weight multiplicity by Berenstein and Zelevinsky. This is based on joint work with Yibo Gao.

Friday 3/15
No seminar - Spring Break

Friday 3/22
JianPing Pan (North Carolina State U.) (Zoom talk)
Title TBA

Friday 3/29
Dania Morales
Title TBA

Friday 4/5
Aaron Ortiz
Title TBA

Friday 4/12
Mark Denker
Title TBA

Friday 4/19

Friday 4/26

Friday 5/3 (Stop Day)

For seminars from previous semesters, please see the KU Combinatorics Group page.

Last updated 3/4/24