Discrete Morse Theory and Commutative Algebra

The summer school will focus on recent developments in combinatorial topology and discrete geometry, with an emphasis on the interaction with toric geometry and commutative algebra. A promising contemporary method for getting simple explicit descriptions of topological spaces is discrete Morse theory. Its applications range from real world problems, such as shape recognition, to theoretical studies of topological spaces, which encode important invariants from algebra, geometry and topology. Program participants will learn how to use these state-of-the-art tools to investigate a variety of topics such as: complements of hyperplane arrangements, resolutions of monomial and toric ideals, knots in triangulated manifolds, metric structures on simplicial complexes, spaces realizing desired cohomology rings, and topological representations of matroids.