Results 1  10
of
14
Polynomiality of hurwitz numbers, bouchardmario conjecture, and a new proof of the elsv formula. arXiv:1307.4729
, 2013
"... ar ..."
(Show Context)
QUANTUM SPECTRAL CURVE FOR THE GROMOVWITTEN THEORY OF THE COMPLEX PROJECTIVE LINE
"... Abstract. We construct the quantum curve for the GromovWitten theory of the complex projective line. Contents ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We construct the quantum curve for the GromovWitten theory of the complex projective line. Contents
QUANTUM CURVES FOR HITCHIN FIBRATIONS AND THE EYNARDORANTIN THEORY
, 2014
"... 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 the topological recursion, which is defined to be a complex plane curve, is replaced with a generic ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
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 the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle T ∗C of an arbitrary smooth base curve C. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal deformation family of D modules over an arbitrary projective algebraic curve C of genus greater than 1, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the SL(2,C)character variety of the fundamental group π1(C). We show that the semiclassical limit through the WKB approximation of these deformed D
QUANTUM CURVES AND TOPOLOGICAL RECURSION
"... ABSTRACT. This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schrödinger operatorlike noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way. The Schrödinger oper ..."
Abstract
 Add to MetaCart
(Show Context)
ABSTRACT. This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schrödinger operatorlike noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way. The Schrödinger operator annihilates a wave function which can be constructed using the WKB method, and conjecturally constructed in a rather different way via topological recursion. CONTENTS
3 EQUIVALENCE OF ELSV AND BOUCHARDMARIÑO CONJECTURES FOR rSPIN HURWITZ NUMBERS
"... ar ..."
(Show Context)
Abstract loop equations, topological recursion and applications
"... We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The SchwingerDyson equation of the one and two hermitian matrix models, and of the Opnq model appear as sp ..."
Abstract
 Add to MetaCart
We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The SchwingerDyson equation of the one and two hermitian matrix models, and of the Opnq model appear as special cases. We study applications to repulsive particles systems, and explain how our notion of loop equations are related to Virasoro constraints. Then, as a special case, we study in detail applications to enumeration problems in a general class of nonintersecting loop models on the random lattice of all topologies, to SUpNq ChernSimons invariants of torus knots in the large N expansion. We also mention an application to Liouville theory on surfaces of positive genus. 1
THE EYNARDORANTIN RECURSION AND EQUIVARIANT MIRROR SYMMETRY FOR THE PROJECTIVE LINE
"... ar ..."
(Show Context)
unknown title
"... Quantum curves for the enumeration of ribbon graphs and hypermaps ..."
(Show Context)