What can chicken nuggets tell us about symmetric functions, positive polynomials, random norms, and AF algebras? (Stephan Garcia, Pomona)

A simple question about chicken nuggets connects everything from analysis and combinatorics to probability theory and computer-aided design.  With tools from complex, harmonic, and functional analysis, probability theory, algebraic combinatorics, and spline theory, we answer many asymptotic questions about factorization lengths in numerical semigroups.  Our results yield uncannily accurate predictions, along with unexpected results about symmetric functions, trace polynomials, and the statistical properties of certain AF C$^*$-algebras.