Abstract.
Numerical semigroups are simple cofinite additive submonoids of the natural numbers, yet their associated semigroup rings reveal rich structures in commutative algebra. Through toric ideals, associated graded rings, and free resolutions, questions about presentations and defining relations can be translated into problems on Betti numbers, syzygies, and related algebraic invariants. This talk gives a brief introduction to this viewpoint and presents several problems concerning relations of numerical semigroups and their semigroup rings.
