## 31 Citations

### Rational reductions of the 2D-Toda hierarchy and mirror symmetry

- MathematicsJournal of the European Mathematical Society
- 2017

We introduce and study a two-parameter family of symmetry reductions of the two-dimensional Toda lattice hierarchy, which are characterized by a rational factorization of the Lax operator into a…

### A modified melting crystal model and the Ablowitz–Ladik hierarchy

- Mathematics
- 2013

This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expressed as the vacuum…

### Open Topological Strings and Integrable Hierarchies: Remodeling the A-Model

- Mathematics
- 2011

We set up, purely in A-model terms, a novel formalism for the global solution of the open and closed topological A-model on toric Calabi-Yau threefolds. The starting point is to build on recent…

### INTEGRABLE SYSTEMS AND MODULI SPACES OF CURVES

- Mathematics
- 2016

This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and…

### The open string McKay correspondence for type A singularities

- Mathematics
- 2013

We formulate a Crepant Resolution Correspondence for open Gromov-Witten invariants (OCRC) of toric Calabi-Yau orbifolds by viewing the open theories as sections of Givental's symplectic vector space…

### Tri-Hamiltonian structure of the Ablowitz–Ladik hierarchy

- MathematicsPhysica D: Nonlinear Phenomena
- 2022

### Orbifold melting crystal models and reductions of Toda hierarchy

- Mathematics
- 2014

Orbifold generalizations of the ordinary and modified melting crystal models are introduced. They are labelled by a pair a , b ?> of positive integers, and geometrically related to Z a × Z b ?>…

### Old and New Reductions of Dispersionless Toda Hierarchy

- Mathematics
- 2012

This paper is focused on geometric aspects of two particular types of finite- variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of \Landau{Ginzburg…

### Extended r-spin theory in all genera and the discrete KdV hierarchy

- MathematicsAdvances in Mathematics
- 2021

### Toda hierarchies and their applications

- Mathematics
- 2018

The 2D Toda hierarchy occupies a central position in the family of integrable hierarchies of the Toda type. The 1D Toda hierarchy and the Ablowitz–Ladik (aka relativistic Toda) hierarchy can be…

## References

SHOWING 1-10 OF 59 REFERENCES

### Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

- Mathematics
- 2001

We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the…

### ORBIFOLD QUANTUM COHOMOLOGY OF THE CLASSIFYING SPACE OF A FINITE GROUP

- Mathematics
- 2001

We work through, in detail, the quantum cohomology, with gravi- tational descendants, of the orbifold BG, the point with action of a finite group G. We provide a simple description of algebraic…

### Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz–Ladik hierarchy

- Mathematics
- 2009

Adler and van Moerbeke (2001 Commun. Pure Appl. Math. 54 153–205) described a reduction of the 2D-Toda hierarchy called the Toeplitz lattice. This hierarchy turns out to be equivalent to the one…

### The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies

- Mathematics
- 2008

Abstract Let Mk,m be the space of Laurent polynomials in one variable , where k,m ≧ 1 are fixed integers and . According to B. Dubrovin [B. Dubrovin, Geometry of 2d topological field theories,…

### Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations

- Mathematics
- 2008

We compute, with symplectic field theory (SFT) techniques, the Gromov-Witten theory of $${\mathbb{P}^1_{\alpha_1,\ldots,\alpha_a}}$$, i.e., the complex projective line with a orbifold points. A…

### A bi-Hamiltonian structure for the integrable, discrete non-linear Schrödinger system

- Mathematics
- 2006

### On classification ofN=2 supersymmetric theories

- Mathematics, Physics
- 1993

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling…

### Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models

- Physics
- 1992

We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii hierarchy is involved in the Landau-Ginsburg topological models (forAn-Series): the Casimirs for the first P.B. give the…