Date: 8th May, 2026
Venue: Rm. 207, Bldg. 10, SNU
Invited Speakers
Minho Cho (KIAS)
Cheolwon Heo (SUNY Korea)
Kang-Ju Lee (SNU)
This mini-workshop consists of three invited talks on matroids and related topics.
Program
13:00-13:30 Registration & Opening
13:30-14:30 Cheolwon Heo, Recognizing even-cycle and even-cut matroids
Even-cycle matroids are elementary lifts of graphic matroids and even-cut matroids are elementary lifts of cographic matroids. In this talk, we present a polynomial algorithm to check if a binary matroid is an even-cycle matroid and we present a polynomial algorithm to check if a binary matroid is an even-cut matroid. These two algorithms rely on a polynomial algorithm to check if a binary matroid is pinch-graphic.
14:40-15:40 Kang-Ju Lee, Tutte Polynomials and Matroid Complexes
Tutte polynomials are fundamental invariants in matroid theory, defined via the deletion–contraction recursion. Their specializations recover numerous important invariants, including the number of spanning trees and the chromatic polynomial. In particular, we focus on specializations related to the face enumerator and the $h$-polynomial of matroid complexes, together with a combinatorial interpretation of the coefficients of the $h$-polynomial. We present a formula for the simplicial tree-numbers of matroid complexes in terms of these specializations of the Tutte polynomial.
15:40-16:00 Coffee Break
16:00-17:00 Minho Cho, Colorful circuits and colorful topes in oriented matroids
Abstract: We list some rainbow problems in graph theory, matroid theory and oriented matroid theory. As a partial result, we obtain a "rainbow tope" result which implies a rainbow problem on words. The key lemma is a common generalization of Sperner's theorem and Meshulam's lemma, each of which guarantees the existence of rainbow simplexes in vertex-colored simplicial complexes under different assumptions. We follow the same approach to analyze structures of rainbow (co)circuits of oriented matroids. Using a similar proof technique, we provide an oriented matroid version of Bárány's colorful conic Carathéodory theorem. This is joint work with Frédéric Meunier and Seunghun Lee.
Contact: ds3mbc@snu.ac.kr