Algebraic Combinatorics - William Slofstra

Title: Indicence groups of graphs, forbidden minors, and planar covers

Abstract:

The solution group of binary linear system is a quantum-probabilistic generalization of the solution space of the system. An incidence group is a solution group where the linear system comes from the incidence matrix of a graph. Incidence groups can be defined quite naturally in terms of the underlying graph, and appear to walk an interesting line: they are much more tractable than the class of all solution groups, but still have a non-trivial theory, which is closely connected with the theory of graph minors. In this talk, I'll review what twe know about incidence groups, and give a number of open problems. Contains joint work with Cnnor Paddock, Vincent Russo, and Turner Silverthorne.