Numerical semigroups, minimal presentations, and posets (Chris O’Neill, SDSU)

A numerical semigroup is a subset S of the natural numbers that is closed under addition.  One of the primary attributes of interest in commutative algebra are the relations (or trades) between the generators of S; any particular choice of minimal trades is called a minimal presentation of S (this is equivalent to choosing a minimal binomial generating set for the defining toric ideal of S).  In this talk, we present a method of constructing a minimal presentation of S from a portion of its divisibility poset.  Time permitting, we will explore connections to polyhedral geometry.

No familiarity with numerical semigroups or toric ideals will be assumed for this talk.