32 citations · 187 across the 32 of their papers we have counts for
24 papers · 1 filter
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…
On the large genus of Hurwitz numbers
Davide Accadia, Danilo Lewański, Giulio Ruzza
Hurwitz theory provides a large variety of enumerative problems related to algebraic geometry, mathematical physics, and combinatorics. We give a general framework to approach the…
Invariants of nested Hilbert and Quot schemes on surfaces
Nadir Fasola, Michele Graffeo, Danilo Lewański +1
Let be a smooth pointed surface. In the first part of this paper we study motivic invariants of punctual nested Hilbert schemes attached to using the Hilbert-Samuel…
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…
Les Houches lecture notes on moduli spaces of Riemann surfaces
Alessandro Giacchetto, Danilo Lewański
In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory,…
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-…
On ELSV-type formulae and relations between -integrals via deformations of spectral curves
Gaëtan Borot, Maksim Karev, Danilo Lewański
The general relation between Chekhov-Eynard-Orantin topological recursion and the intersection theory on the moduli space of curves, the deformation techniques in topological recur…
Resurgent large genus asymptotics of intersection numbers
Bertrand Eynard, Elba Garcia-Failde, Alessandro Giacchetto +2
In this paper, we present a novel approach for computing the large genus asymptotics of intersection numbers. Our strategy is based on a resurgent analysis of the -point functio…
The Spin Gromov-Witten/Hurwitz correspondence for
Alessandro Giacchetto, Reinier Kramer, Danilo Lewański +1
We study the spin Gromov-Witten (GW) theory of . Using the standard torus action on , we prove that the associated equivariant potential can be expresse…
An intersection-theoretic proof of the Harer-Zagier formula
Alessandro Giacchetto, Danilo Lewański, Paul Norbury
We provide an intersection-theoretic formula for the Euler characteristic of the moduli space of smooth curves. This formula reads purely in terms of Hodge integrals and, as a coro…
On some hyperelliptic Hurwitz-Hodge integrals
Danilo Lewański
This short note addresses Hodge integrals over the hyperelliptic locus. Recently Afandi computed, via localisation techniques, such one-descendant integrals and showed that they ar…
A natural basis for intersection numbers
Bertrand Eynard, Danilo Lewański
We advertise elementary symmetric polynomials as the natural basis for generating series of intersection numbers of genus g and n marked points. Closed formulae for…
On the Goulden-Jackson-Vakil conjecture for double Hurwitz numbers
Norman Do, Danilo Lewański
Goulden, Jackson and Vakil observed a polynomial structure underlying one-part double Hurwitz numbers, which enumerate branched covers of with prescribed ramificati…
Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
Gaëtan Borot, Norman Do, Maksim Karev +2
Double Hurwitz numbers enumerate branched covers of with prescribed ramification over two points and simple ramification elsewhere. In contrast to the single case,…
Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
D. Chen, M. Möller, A. Sauvaget +3
We describe a conjectural formula via intersection numbers for the Masur-Veech volumes of strata of quadratic differentials with prescribed zero orders, and we prove the formula fo…
Wall-crossing and recursion formulae for tropical Jucys covers
Marvin Anas Hahn, Danilo Lewanski
In recent work, the authors derived a tropical interpretation of monotone and strictly monotone double Hurwitz numbers. In this paper, we apply the technique of tropical flows to t…
Harer-Zagier formula via Fock space
Danilo Lewanski
The goal of this note is to provide a very short proof of Harer-Zagier formula for the number of ways of obtaining a genus g Riemann surface by identifying in pairs the sides of a…
Tropical Jucys Covers
Marvin Anas Hahn, Danilo Lewanski
We study monotone and strictly monotone Hurwitz numbers from a bosonic Fock space perspective. This yields to an interpretation in terms of tropical geometry involving local multip…
Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and simple double Hurwitz numbers
Marvin Anas Hahn, Reinier Kramer, Danilo Lewanski
We derive explicit formulae for the generating series of mixed Grothendieck dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge formalism. This reveals th…
On ELSV-type formulae, Hurwitz numbers and topological recursion
Danilo Lewanski
We present several recent developments on ELSV-type formulae and topological recursion concerning Chiodo classes and several kind of Hurwitz numbers. The main results appeared in D…
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…
-algebra constraints and topological recursion for -singularity
Todor Milanov, Danilo Lewanski
We derive a Bouchard--Eynard type topological recursion for the total descendant potential of -singularity. Our argument relies on a certain twisted representation of a Heisen…