119 citations · 564 across the 26 of their papers we have counts for
32 papers
In Search of a Hidden Curve
Motohico Mulase
It has been noticed since around 2007 that certain enumeration problems can be solved when an analytic or algebraic curve is identified. This curve is the key to the problem. In th…
Mirror curve of orbifold Hurwitz numbers
Olivia Dumitrescu, Motohico Mulase
Edge-contraction operations form an effective tool in various graph enumeration problems, such as counting Grothendieck's dessins d'enfants and simple and double Hurwitz numbers. T…
An invitation to 2D TQFT and quantization of Hitchin spectral curves
Olivia Dumitrescu, Motohico Mulase
This article consists of two parts. In Part 1, we present a formulation of two-dimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs…
Interplay between opers, quantum curves, WKB analysis, and Higgs bundles
Olivia Dumitrescu, Motohico Mulase
Quantum curves were introduced in the physics literature. We develop a mathematical framework for the case associated with Hitchin spectral curves. In this context, a quantum curve…
Opers versus nonabelian Hodge
Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis +3
For a complex simple simply connected Lie group , and a compact Riemann surface , we consider two sorts of families of flat -connections over . Each family is determine…
Lectures on the topological recursion for Higgs bundles and quantum curves
Olivia Dumitrescu, Motohico Mulase
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subj…