160 citations · 1.4k across the 97 of their papers we have counts for
36 papers · 1 filter
A prismatic Riemann-Hilbert correspondence
Dylan Pentland
We study the category of constructible -Kummer-étale sheaves on the log adic generic fiber for the stratification induced by a horizont…
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…
A new family of weighted double Hurwitz numbers and a new ELSV-type formula with -classes
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We analyze a new family of weighted double Hurwitz numbers that was introduced as a notable example in the context of the duality for logarithmic topological recursion. We us…
The quantum integrable hierarchy for the Gromov-Witten theory of elliptic curves
Paolo Rossi, Sergey Shadrin, Ishan Jaztar Singh
We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbe…
A new spin on polynomial relations among kappa classes
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski +2
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algeb…
Theta classes: generalized topological recursion, integrability and -constraints
Vincent Bouchard, Nitin K. Chidambaram, Alessandro Giacchetto +1
We study the intersection theory of the -classes, where and , which are cohomological field theories obtained as the top degrees of Chiodo clas…
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…
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…
Taking limits in topological recursion
Gaëtan Borot, Vincent Bouchard, Nitin Kumar Chidambaram +2
When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectra…
Tautological relations and integrable systems
Alexandr Buryak, Sergey Shadrin
We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus with marked points. A large part of the…
A conjectural formula for
Alexandr Buryak, Francisco Hernández Iglesias, Sergey Shadrin
We propose a conjectural formula for and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named…
Deformation theory of Cohomological Field Theories
Vladimir Dotsenko, Sergey Shadrin, Arkady Vaintrob +1
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This le…
Topological recursion for monotone orbifold Hurwitz numbers: a proof of the Do-Karev conjecture
Reinier Kramer, Alexandr Popolitov, Sergey Shadrin
We prove the conjecture of Do and Karev that the monotone orbifold Hurwitz numbers satisfy the Chekhov-Eynard-Orantin topological recursion.
Loop equations and a proof of Zvonkine's -ELSV formula
Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov +1
We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called -ELSV formu…
Buryak-Okounkov formula for the -point function and a new proof of the Witten conjecture
Alexander Alexandrov, Francisco Hernández Iglesias, Sergey Shadrin
We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the e…
Cut-and-join equation for monotone Hurwitz numbers revisited
Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov +1
We give a new proof of the cut-and-join equation for the monotone Hurwitz numbers, derived first by Goulden, Guay-Paquet, and Novak. Our proof in particular uses a combinatorial te…
The tautological ring of via Pandharipande-Pixton-Zvonkine -spin relations
Reinier Kramer, Farrokh Labib, Danilo Lewanski +1
We use relations in the tautological ring of the moduli spaces derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the -s…
Primary invariants of Hurwitz Frobenius manifolds
Petr Dunin-Barkowski, Paul Norbury, Nicolas Orantin +2
Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifold…
Toric varieties of Loday's associahedra and noncommutative cohomological field theories
Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette
We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumfor…
Top tautological group of
A. Buryak, S. Shadrin, D. Zvonkine
We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus curves with marked points.