5 Day Workshop at BIRS — Interactions Between Topological Combinatorics and Combinatorial Commutative Algebra

Two groups of mathematicians, who specialize either in topological combinatorics or in combinatorial commutative algebra, are organizing a workshop in order to identify and to work on problems in the intersection of both fields. Topological combinatorics uses tools from topology to study discrete structures, while combinatorial commutative algebra also studies discrete structures but uses algebraic tools. As a result, the two groups of mathematicians may be studying the exact same problem about discrete structures, but using completely different tools and mathematical language. As an example, questions about the enumeration of the faces of a topological object called a Cohen--Macaulay flag complex can be translated into questions about Hilbert functions of ideals. The goal of this workshop is to bring together 21 mathematicians in both fields to facilitate discussions and encourage new collaborations between these two groups. The organizers have identified five possible themes that will bring an additional focus to the direction of the workshop.