Combinatorial Algebraic Topology & Applications IV

Khovanov-like categorifications of polynomials in matroid theory

Not scheduled

1h

Aula Dini (Palazzo del Castelletto)

Speaker

So Yamagata (Fukuoka University)

Description

Khovanov introduced a bigraded cohomology theory for links whose graded Euler characteristic recovers the Jones polynomial. Analogous Khovanov-like (co)homology theories have since been developed beyond knot theory, including chromatic cohomology for graphs and characteristic homology for hyperplane arrangements.
A matroid is a combinatorial structure that captures abstract notions of dependence, encompassing cycles in graphs and linear dependencies of vectors. In particular, matroids arise naturally from both graphs and hyperplane arrangements.
In this talk, we introduce (co)homology groups associated with certain polynomials of matroids. This is joint work with Takuya Saito.