32 citations · 140 across the 26 of their papers we have counts for
4 papers · 1 filter
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…
Lusztig Factorization Dynamics of the Full Kostant-Toda Lattices
Nicholas M. Ercolani, Jonathan Ramalheira-Tsu
We study extensions of the classical Toda lattices at several different space-time scales. These extensions are from the classical tridiagonal phase spaces to the phase space of fu…
Ginzburg-Landau Equations on Non-compact Riemann Surfaces
Nicolas M. Ercolani, Israel Michael Sigal, Jingxuan Zhang
We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less…