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Numerical semigroups, minimal presentations, and posets

Christopher O'Neill, San Diego State University
Wednesday, December 6, 2023 - 3:30pm to 5:00pm
PDL C-401 and via Zoom Link:
Christopher O'Neill
Christopher O'Neill


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. 

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00, as detailed below. The main talk starts at 4:10.

Pre-seminar: The combinatorics of polyhedra

When someone refers to "the combinatorics" of a polyhedron, they usually mean its face lattice, i.e., its collection of faces, ordered by containment.  In this pre-seminar talk, we will explore several well-studied families of polyhedra whose face lattices also arise in enumerative combinatorics. 

Join Zoom Meeting:
Meeting ID: 915 4733 5974