The Cox ring of a projective variety is the ring of all its meromorphic functions, together with a grading of geometric origin. Determining whether this ring is finitely generated is a challenging task, even for simple examples. In this talk, we will discuss our efforts to tackle this problem for a specific class of varieties, […]

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 […]