Spring 2024

- The Combinatorics Seminar meets on
**Fridays, 3-4pm**, in**Snow 306**(including talks on Zoom). There will be cookies! - Organizers: Jeremy Martin, Mark Denker, Reuven Hodges, and Marge Bayer.
- Good general seminar-attending advice, especially for graduate students: The "Three Things" Exercise for getting things out of talks by Ravi Vakil
- Also consider attending the Graduate Online Combinatorics Colloquium.

**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**

TBA

**Friday 4/26**

TBA

**Friday 5/3 (Stop Day)**

TBA

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

Last updated 3/4/24