8 papers
Triple Hodge integrals and constant Poisson brackets for rank-one Dubrovin-Zhang hierarchies
Xavier Blot, Guido Carlet, Dimitrios Makris +1
We prove a conjecture of Dubrovin, Liu, Yang, and Zhang that states that the Poisson bracket of the Dubrovin-Zhang hierarchy of a rank-one cohomological field theory is constant if…
Beyond descendants: integrable observables for cohomological field theories
Xavier Blot, Danilo LewaÅski, Sergey Shadrin
We introduce the concept of integrable observables and propose them as alternatives to the standard Witten's psi classes (a.k.a. descendants in quantum gravity) to be coupled…
Equivalence of quantizations of the dispersionless KdV hierarchy
Xavier Blot
Wang recently constructed a quantization of the dispersionless KdV hierarchy using the Heisenberg vertex algebra. Independently, in joint work with Rossi, we obtained a quantizatio…
Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT
Xavier Blot, Paolo Rossi, Adrien Sauvaget
In [arXiv:2408.13806], two families of classical and quantum integrable hierarchies associated to arbitrary Cohomological Field Theories (CohFTs) were introduced: the meromorphic d…
Quantum intersection numbers and the Gromov-Witten invariants of
Xavier Blot, Alexandr Buryak
The notion of a quantum tau-function for a natural quantization of the KdV hierarchy was introduced in a work of Dubrovin, Guéré, Rossi, and the second author. A certain natural…
On the strong DR/DZ equivalence conjecture
Xavier Blot, Danilo Lewanski, Sergey Shadrin
We establish the Miura equivalence of two integrable systems associated to a semi-simple cohomological field theory: the double ramification hierarchy of Buryak and the Dubrovin-Zh…