November 10, 2010
Thomas Kahle, Institut Mittag-Leffler: A taxonomy of commutative monoid congruences
Abstract:
Recent research on the combinatorics of binomial ideals has
renewed interest in congruences on commutative Noetherian monoids. Each
binomial ideal in a monoid algebra defines a congruence on the monoid,
and decompositions of the congruence correspond to decompositions of the
binomial ideal. In 1963 primary decompositions of congruences on
commutative Noetherian monoids have been described by Karel Drbohlav.
As it turns out, these are not fine enough for an understanding of the
combinatorics of a given binomial ideal. In this talk we discuss how to
extend and adapt Drbohlav's theory such that it suits for an
understanding of lattice point geometries of binomial ideals.