Geometric and Enumerative Combinatorics

Enumerative combinatorics, or the mathematics of counting, has broad applications in probability, statistical physics, optimization, and computer science. Its problems require the strategic application of tools from many other areas of mathematics and, in recent years, have stimulated the development of many new results and tools. Geometric combinatorics focuses on discrete objects with geometric or topological structure, such as convex polytopes, arrangements of vectors, points, subspaces, and partially ordered sets. These give rise to counting problems that are sometimes hard even to estimate, and sometimes involve objects with interesting symmetry groups, giving rise to new combinatorics. The purpose of this workshop is to bring together researchers in the areas of geometric combinatorics and enumerative combinatorics to present new results and plan for further progress. It will include researchers from applications areas that supply some of the challenging problems for the field. In addition, it will include researchers who are developing innovative computational tools for enumeration. The organizers will take advantage of the local strength and tradition (both at the University of Minnesota and surrounding schools) in algebraic, geometric, and enumerative combinatorics.