This will be a
course about exciting new developments at the intersection of
Commutative Algebra and Combinatorics and connections to such diverse
areas as Toric Geometry, Homological Algebra, Graph Theory, and
Symbolic Computation. The main players on the algebra side will be
monomial ideals, i.e. ideals generated by monomials, and toric ideals,
i.e. ideals generated by differences of two monomials. On the
combinatorics side, graphs, polytopes, and simplicial complexes will
figure prominently. The focus will be on numerical invariants,
their interpretations and computation.
