Commutative Algebra Seminar in Beijing | Toric Alqebras and Matroids

Abstract

In the first lecture I will give an introduction to toric algebras. toric algebra can be seen as a monomial subalgebra, or as a quotient of apolynomial ring by a binomialprime ideal. We will discuss how to move between these two presentations, and compute the Krull dimension of a torialgebra. The monomial preentation provides a link betwen combinatorial obiects and algebraic structures. The second lecture will be dedicated totoric algebras arising from a particular type of combinatorial obiects, namely matroids. Whites conjecture suggests a connection between a certainexchange property on matroids, and ther associated binomial ideals. We will discuss solved and unsolved instances of this intriquing open problem.