## 4 Citations

### 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,…

### 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…

### 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…

### The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one

- Mathematics
- 2021

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

## References

SHOWING 1-10 OF 45 REFERENCES

### 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…

### Double Ramification Cycles and Quantum Integrable Systems

- Mathematics
- 2015

In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085–1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersection…

### Recursion Relations for Double Ramification Hierarchies

- Mathematics
- 2014

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in Buryak (CommunMath Phys 336(3):1085–1107, 2015) using…

### BCFG Drinfeld–Sokolov hierarchies and FJRW-theory

- Mathematics
- 2013

According to the ADE Witten conjecture, which is proved by Fan, Jarvis and Ruan, the total descendant potential of the FJRW invariants of an ADE singularity is a tau function of the corresponding…

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

- Computer Science, Mathematics
- 2015

### The structure of 2D semi-simple field theories

- Mathematics
- 2012

I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to the…

### Soliton equations, vertex operators, and simple singularities

- Mathematics
- 2009

We prove the equivalence of two hierarchies of soliton equations associated to a simply-laced finite Dynkin diagram. The first was defined by Kac and Wakimoto (Proc. Symp. Pure Math. 48:138–177,…

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

- MathematicsAdvances in Mathematics
- 2021

### Witten’s D4 integrable hierarchies conjecture

- Mathematics
- 2010

The authors prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D4 with symmetry group 〈J〉 and for D4T with symmetry group Gmax, respectively, are both…