South African - Japanese Discrete Homotopy Meeting 2025 (Cape Town, South Africa, 10-11 September 2025)

10th of September 2025  - 09.50/10.30  

Venue: MAM111 - Department of Mathematics and Applied Mathematics - University of Cape Town

Speaker:   Takuya Saito (Hokkaido University, Hokkaido, Japan)

Title:          A categorification of polynomial invariants of matroids

Abstract:  A matroid is a combinatorial structure that generalizes concepts such as the cycle structure of a graph and the linear independence of a set of vectors. Its polynomial invariants possess a rich theoretical framework. For example, invariants such as the chromatic and flow polynomials of graphs, the characteristic polynomials of hyperplane arrangements, and the weight enumerators of linear codes can all be treated in a unified manner via matroids. In this talk, I will introduce a categorification of polynomial invariants of matroids, motivated by an analogy with Khovanov homology. This presentation is based on joint work with So Yamagata (Fukuoka University).