# Towards a description of the double ramification hierarchy for Witten's $r$-spin class

@article{Buryak2015TowardsAD, title={Towards a description of the double ramification hierarchy for Witten's \$r\$-spin class}, author={Alexandr Buryak and J'er'emy Gu'er'e}, journal={arXiv: Mathematical Physics}, year={2015} }

## 15 Citations

### Integrable Systems of Double Ramification Type

- MathematicsInternational Mathematics Research Notices
- 2019

In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the 1st author, and its quantization. We extend the notion of tau-symmetry to quantum integrable…

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

- MathematicsAdvances in Mathematics
- 2021

### Tau-Structure for the Double Ramification Hierarchies

- MathematicsCommunications in Mathematical Physics
- 2018

In this paper we continue the study of the double ramification hierarchy of Buryak (Commun Math Phys 336(3):1085–1107, 2015). After showing that the DR hierarchy satisfies tau-symmetry we define its…

### Tau-Structure for the Double Ramification Hierarchies

- MathematicsCommunications in Mathematical Physics
- 2018

In this paper we continue the study of the double ramification hierarchy of Buryak (Commun Math Phys 336(3):1085–1107, 2015). After showing that the DR hierarchy satisfies tau-symmetry we define its…

### The Bi-Hamiltonian Structures of the DR and DZ Hierarchies in the Approximation up to Genus One

- MathematicsFunctional Analysis and Its Applications
- 2021

In a recent paper, given an arbitrary homogeneous cohomological field theory ( CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space of local functionals,…

### Quantum D4 Drinfeld–Sokolov hierarchy and quantum singularity theory

- MathematicsJournal of Geometry and Physics
- 2019

### Integrability, Quantization and Moduli Spaces of Curves

- Mathematics
- 2017

This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the…

### Equivariant Landau--Ginzburg mirror symmetry

- Mathematics
- 2019

We give a new proof of the computation of Hodge integrals we have previously obtained for the quantum singularity (FJRW) theory of chain polynomials. It uses the classical localization formula of…

### Hodge integrals in FJRW theory

- Mathematics
- 2015

We study higher genus Fan--Jarvis--Ruan--Witten theory of any chain polynomial with any group of symmetries. Precisely, we give an explicit way to compute the cup product of Polishchuk and Vaintrob's…

### Towards a bihamiltonian structure for the double ramification hierarchy

- MathematicsLetters in Mathematical Physics
- 2021

We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field…

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