## 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

### 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…

### 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…

### Enumerative geometry of surfaces and topological strings

- Mathematics
- 2022

This survey covers recent developments on the geometry and physics of Looijenga pairs, namely pairs (X,D) with X a complex algebraic surface and D a singular anticanonical divisor in it. I will…

### Modified melting crystal model and Ablowitz-Ladik hierarchy

- Physics
- 2014

This is a review of recent results on the integrable structure of the ordinary and modified melting crystal models. When deformed by special external potentials, the partition function of the…

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- Mathematics
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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…

### 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…

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- Mathematics
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- 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…

### Integrable hierarchies and dispersionless limit

- Mathematics
- 1995

Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical…