32 citations · 140 across the 26 of their papers we have counts for
26 papers
Yang-Mills-Higgs Equations on Spherical Orbifolds
Nicholas M. Ercolani
In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connec…
Total positivity and spectral theory for Toeplitz Hessenberg matrix ensembles
Nicholas Ercolani, John Peca-Medlin, Jonathan Ramalheira-Tsu
In this paper we define and lay the groundwork for studying a novel matrix ensemble: totally positive Hessenberg Toeplitz operators, denoted TPHT. This is the intersection of two e…
Map enumeration from a dynamical perspective
Nicholas Ercolani, Joceline Lega, Brandon Tippings
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlevé equations) and asymptotic analysis of orthogonal poly…
The Poisson Geometry of Plancherel Formulas for Triangular Groups
Nicholas M. Ercolani
In this paper we establish the existence of canonical coordinates for generic co-adjoint orbits on triangular groups. These orbits correspond to a set of full Plancherel measure on…
Non-recursive Counts of Graphs on Surfaces
Nicholas Ercolani, Joceline Lega, Brandon Tippings
The problem of map enumeration concerns counting connected spatial graphs, with a specified number of vertices, that can be embedded in a compact surface of genus in such a…
Multiple Scale Asymptotics of Map Enumeration
Nicholas Ercolani, Joceline Lega, Brandon Tippings
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar…