7 citations · 14 across the 14 of their papers we have counts for
14 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 Lewański, 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…
Faber's socle intersection numbers via Gromov--Witten theory of elliptic curve
Xavier Blot, Sergey Shadrin, Ishan Jaztar Singh
The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of . This new proof exhibits a…
Cohomological representations of quantum tau functions
Xavier Blot, Danilo Lewański, Sergey Shadrin
In 2016, Buryak and Rossi introduced the quantum Double Ramification (DR) hierarchies which associate a quantum integrable hierarchy to any Cohomological Field Theory (CohFT). Shor…
Meromorphic differentials, twisted DR cycles and quantum integrable hierarchies
Xavier Blot, Paolo Rossi
We define twisted versions of the classical and quantum double ramification hierarchy construction based on intersection theory of the strata of meromorphic differentials in the mo…
The master relation for polynomiality and equivalences of integrable systems
Xavier Blot, Adrien Sauvaget, Sergey Shadrin
We prove the so-called master relation in the tautological ring of the moduli space of curves that implies polynomial properties of the Dubrovin-Zhang hierarchies associated to dif…
Rooted trees with level structures, -classes and double ramification cycles
Xavier Blot, Danilo Lewański, Sergey Shadrin
We prove a new system of relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by the top Chern class of the…
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…
Stable tree expressions with Omega-classes and Double Ramification cycles
Xavier Blot, Danilo Lewański, Paolo Rossi +1
We propose a new system of conjectural relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by Hodge and Ω-…
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 ch…
The amplituhedron crossing and winding numbers
Xavier Blot, Jian-Rong Li
In \cite{arkani2018unwinding}, Arkani-Hamed, Thomas and Trnka formulated two conjectural descriptions of the tree amplituhedron $\ampli$ depending on the parity of . When is…
The quantum Witten-Kontsevich series and one-part double Hurwitz numbers
Xavier Blot
We study the quantum Witten-Kontsevich series introduced by Buryak, Dubrovin, Guéré and Rossi in \cite{buryak2016integrable} as the logarithm of a quantum tau function for the quan…