3 papers
math.GT2025
Volume bounds for hyperbolic rod complements in the 3-torus
Norman Do, Connie On Yu Hui, Jessica S. Purcell
The study of rod complements is motivated by rod packing structures in crystallography. We view them as complements of links comprised of Euclidean geodesics in the 3-torus. Recent…
math.CO2025
From Weingarten calculus for real Grassmannians to deformations of monotone Hurwitz numbers and Jucys-Murphy elements
Xavier Coulter, Norman Do
The present work is inspired by three interrelated themes: Weingarten calculus for integration over unitary groups, monotone Hurwitz numbers which enumerate certain factorisations…
math.CO2024
The structure of Hurwitz numbers with fixed ramification profile and varying genus
Norman Do, Jian He, Heath Robertson
In 1891, Hurwitz introduced the enumeration of genus , degree , branched covers of the Riemann sphere with simple ramification over prescribed points and no branching elsewhe…