Algebraic Combinatorics Seminar

Title: The Many Faces of Circulation Algebras

Abstract:  The circulation algebra is a commutative graded algebra associated to a graph, introduced by Wagner in 1998 to study flows. Its graded dimension is given by a certain specialization of the graph's Tutte polynomial, and it encodes information about the combinatorics of circuits in the graph roughly equivalent to the cycle matroid. Somewhat surprisingly, algebras of essentially the same kind appear in areas as seemingly distant as numerical approximation theory and the geometry of homogeneous manifolds. I will give a survey of the basic theory of these algebras and the different contexts in which they have been studied, including my own research.