# Mathematics Colloquia and Seminars

Then I'll review Robin Forman's discrete Morse theory, Chari's combinatorial reformulation in terms of matchings on face posets, and discuss how this may be applied to monoid posets. When one has a Groebner basis of degree d for a toric ideal related to the monoid, we show that this implies that the homology of each monoid poset interval vanishes below dimension equal to the rank of the interval divided by d-1. This gives a combinatorial version of a notion from commutative algebra in this case -- the complexity of a resolution, and it enables us to construct a correspondingly small'' resolution. This is joint work with Volkmar Welker.