Paolo Rossi
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View article: Meromorphic Differentials, Twisted DR Cycles and Quantum Integrable Hierarchies
Meromorphic Differentials, Twisted DR Cycles and Quantum Integrable Hierarchies Open
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 moduli space of stable curves and k -twisted double ramificat…
View article: Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT
Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT Open
In [arXiv:2408.13806], two families of classical and quantum integrable hierarchies associated to arbitrary Cohomological Field Theories (CohFTs) were introduced: the meromorphic differential and twisted double ramification hierarchies. Fo…
View article: Deformations of the Riemann hierarchy and the geometry of $\overline{\mathcal{M}}_{g,n}$
Deformations of the Riemann hierarchy and the geometry of $\overline{\mathcal{M}}_{g,n}$ Open
The Riemann hierarchy is the simplest example of rank one, ($1$+$1$)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the Korteweg-de Vries hierarchy. In the language of formal var…
View article: Stable tree expressions with Omega-classes and double ramification cycles
Stable tree expressions with Omega-classes and double ramification cycles Open
View article: Meromorphic differentials, twisted DR cycles and quantum integrable hierarchies
Meromorphic differentials, twisted DR cycles and quantum integrable hierarchies Open
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 moduli space of stable curves and $k$-twisted double ramifica…
View article: Bihamiltonian structure of the DR hierarchy in the semisimple case
Bihamiltonian structure of the DR hierarchy in the semisimple case Open
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the secon…
View article: Counting meromorphic differentials on $${\mathbb {C}\mathbb {P}}^1$$
Counting meromorphic differentials on $${\mathbb {C}\mathbb {P}}^1$$ Open
We give explicit formulas for the number of meromorphic differentials on $$\mathbb{C}\mathbb{P}^1$$ with two zeros and any number of residueless poles and for the number of meromorphic differentials on $$\mathbb{C}\mathbb{P}^1$$ …
View article: Stable tree expressions with Omega-classes and Double Ramification cycles
Stable tree expressions with Omega-classes and Double Ramification cycles Open
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-classes and prove these conjectures in different cases.
View article: Stable Tree Expressions with Omega-Classes and Double Ramification Cycles
Stable Tree Expressions with Omega-Classes and Double Ramification Cycles Open
View article: Intersection numbers with Pixton's class and the noncommutative KdV hierarchy
Intersection numbers with Pixton's class and the noncommutative KdV hierarchy Open
The Pixton class is a nonhomogeneous cohomology class on the moduli space of stable curves $\overline{\mathcal{M}}_{g,n}$, with nontrivial terms in degree $0,2,4,\ldots,2g$, whose top degree part coincides with the double ramification cycl…
View article: Semisimple Flat F-Manifolds in Higher Genus
Semisimple Flat F-Manifolds in Higher Genus Open
View article: A GENERALISATION OF WITTEN’S CONJECTURE FOR THE PIXTON CLASS AND THE NONCOMMUTATIVE KDV HIERARCHY
A GENERALISATION OF WITTEN’S CONJECTURE FOR THE PIXTON CLASS AND THE NONCOMMUTATIVE KDV HIERARCHY Open
In this paper, we formulate and present ample evidence towards the conjecture that the partition function (i.e. the exponential of the generating series of intersection numbers with monomials in psi classes) of the Pixton class on the modu…
View article: Moduli spaces of residueless meromorphic differentials and the KP hierarchy
Moduli spaces of residueless meromorphic differentials and the KP hierarchy Open
We prove that the cohomology classes of the moduli spaces of residueless meromorphic differentials, i.e., the closures, in the moduli space of stable curves, of the loci of smooth curves whose marked points are the zeros and poles of presc…
View article: Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics
Riemannian F-Manifolds, Bi-Flat F-Manifolds, and Flat Pencils of Metrics Open
In this paper, we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold, we present a construction of a canonical flat F-manifold associated to it. We also describe a con…
View article: Extended r-spin theory in all genera and the discrete KdV hierarchy
Extended r-spin theory in all genera and the discrete KdV hierarchy Open
View article: A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy
A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy Open
In this paper, we formulate and present ample evidence towards the conjecture that the partition function (i.e. the exponential of the generating series of intersection numbers with monomials in psi classes) of the Pixton class on the modu…
View article: Quadratic double ramification integrals and the noncommutative KdV hierarchy
Quadratic double ramification integrals and the noncommutative KdV hierarchy Open
In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic D…
View article: Quantum <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e19" altimg="si10.gif"><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:math> Drinfeld–Sokolov hierarchy and quantum singularity theory
Quantum Drinfeld–Sokolov hierarchy and quantum singularity theory Open
View article: Simple Lax Description of the ILW Hierarchy
Simple Lax Description of the ILW Hierarchy Open
In this note we present a simple Lax description of the hierarchy of the\nintermediate long wave equation (ILW hierarchy). Although the linear inverse\nscattering problem for the ILW equation itself was well known, here we give an\nexplici…
View article: Extended $r$-spin theory in all genera and the discrete KdV hierarchy
Extended $r$-spin theory in all genera and the discrete KdV hierarchy Open
In this paper we construct a family of cohomology classes on the moduli space\nof stable curves generalizing Witten's $r$-spin classes. They are parameterized\nby a phase space which has one extra dimension and in genus $0$ they correspond…
View article: Integrability, Quantization and Moduli Spaces of Curves
Integrability, Quantization and Moduli Spaces of Curves Open
This paper has the purpose of presenting in an organic way a new approach to\nintegrable (1+1)-dimensional field systems and their systematic quantization\nemerging from intersection theory of the moduli space of stable algebraic\ncurves a…
View article: Rational reductions of the 2D-Toda hierarchy and mirror symmetry
Rational reductions of the 2D-Toda hierarchy and mirror symmetry Open
We introduce and study a two-parameter family of symmetry reductions of the two-dimensional Toda lattice hierarchy, which are characterized by a rational factorization of the Lax operator into a product of an upper diagonal and the inverse…
View article: Integrable systems and moduli spaces of curves
Integrable systems and moduli spaces of curves Open
This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and mirror symmetry. The text contains a sh…
View article: Recursion Relations for Double Ramification Hierarchies
Recursion Relations for Double Ramification Hierarchies Open
View article: Double Ramification Cycles and Quantum Integrable Systems
Double Ramification Cycles and Quantum Integrable Systems Open