Title: Combinatorics and the Kitchen Sink
Abstract: Numerical semigroups are simple combinatorial objects that lead to deep and subtle questions. We answer in one fell swoop virtually all asymptotic questions about factorization lengths in numerical semigroups. Surprisingly, this uses tools from complex, harmonic, and functional analysis, probability theory, algebraic combinatorics, and computer-aided design! Our results yield uncannily accurate predictions that agree with numerical computations, along with some totally unexpected byproducts.
This work was partially supported by NSF Grant DMS-1800123. Joint work with A. Böttcher, M. Omar, C.O’Neill, and Pomona undergraduate students T. Wesley (’21) and S.Yih (’18).
Prof. Garcia is the W.M. Keck Distinguished Service Professor and Professor of Mathematics at Pomona College