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 […]

The Kauffman bracket skein algebra of a surface is at once related to quantum topology and to hyperbolic geometry. In this talk, we consider a generalization of the skein algebra due to Roger and Yang for surfaces with punctures. In joint work with Han-Bom Moon, we show that the generalized skein algebra is a quantization […]

The original Bost-Connes system was constructed in 1990 and is a QSM system with deep connections to the field of rationals. In particular, its partition function is the Riemann-zeta function and its ground states evaluated on certain arithmetic objects yield generators of the maximal Abelian extension of the rationals. In this talk we describe the […]