Combinatorics Seminar-Random Monomial Ideals

Abstract: Randomness is an important tool in algebra and combinatorics. In this talk I will discuss our recent work trying to look at random behavior of monomial and binomial ideals. Inspired by earlier results on random graphs and random simplicial complexes, we develop a theory of random monomial ideals and random semigroups rings. For example, we present theorems about the probability distributions, expectations and thresholds for events of monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers and the projective dimension of those ideals.