Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion

  title={Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion},
  author={Olivier Marchal and Nicolas Orantin},
  journal={Journal of Geometry and Physics},

Witten–Reshetikhin–Turaev Function for a Knot in Seifert Manifolds

In this paper, for a Seifert loop (i.e., a knot in a Seifert three-manifold), first we give a family of explicit functions Φ(q;N)\documentclass[12pt]{minimal} \usepackage{amsmath}



Quantum Curves for Hitchin Fibrations and the Eynard–Orantin Theory

We generalize the topological recursion of Eynard–Orantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347–452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in

Isomonodromic Tau-Functions from Liouville Conformal Blocks

The goal of this note is to show that the Riemann–Hilbert problem to find multivalued analytic functions with $${{\rm SL}(2,\mathbb{C})}$$SL(2,C)-valued monodromy on Riemann surfaces of genus zero

2-Parameter $$\tau $$-Function for the First Painlevé Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis

  • Kohei Iwaki
  • Mathematics
    Communications in Mathematical Physics
  • 2020
We show that a 2-parameter family of $$\tau $$ -functions for the first Painleve equation can be constructed by the discrete Fourier transform of the topological recursion partition function for a

Geometry of Spectral Curves and All Order Dispersive Integrable System

We propose a definition for a Tau function and a spinor kernel (closely related to Baker{Akhiezer functions), where times parametrize slow (of order 1=N) deformations of an algebraic plane curve.

Darboux coordinates and Liouville-Arnold integration in loop algebras

AbstractDarboux coordinates are constructed on rational coadjoint orbits of the positive frequency part $$\tilde{\mathfrak{g}}^+$$ of loop algebras. These are given by the values of the spectral

Loop Algebra Moment Maps and Hamiltonian Models for the Painleve Transcendants

The isomonodromic deformations underlying the Painlev\'e transcendants are interpreted as nonautonomous Hamiltonian systems in the dual $\gR^*$ of a loop algebra $\tilde\grg$ in the classical

Quantum Curve and the First Painlevé Equation

We show that the topological recursion for the (semi-classical) spectral curve of the first Painlev e equation PI gives a WKB solution for the isomonodromy problem for PI. In other words, the

Symplectic geometry of the moduli space of projective structures in homological coordinates

We study the symplectic geometry of the space of linear differential equations with holomorphic coefficients of the form $$\varphi ''-u\varphi =0$$φ′′-uφ=0 on Riemann surfaces of genus g. This space

Painlevé 2 Equation with Arbitrary Monodromy Parameter, Topological Recursion and Determinantal Formulas

The goal of this article is to prove that the determinantal formulas of the Painlevé 2 system identify with the correlation functions computed from the topological recursion on their spectral curve

Lecture notes on topological recursion and geometry

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations,