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

## September 12, 2023 @ 12:15 pm - 1:10 pm

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.