Integrable hierarchies, Frölicher–Nijenhuis bicomplexes and Lauricella bi-flat F-manifolds

P Lorenzoni, S Perletti - Nonlinearity, 2023 - iopscience.iop.org
Given the Frölicher-Nijenhuis bicomplex (d, dL) associated with a (1, 1)-tensor field L with
vanishing Nijenhuis torsion, we define a multi-parameter family of bi-flat structures (∇ …

Tautological relations and integrable systems

A Buryak, S Shadrin - Épijournal de Géométrie Algébrique, 2024 - epiga.episciences.org
We present a family of conjectural relations in the tautological cohomology of the moduli
spaces of stable algebraic curves of genus g with n marked points. A large part of these …

Flat F-manifolds, F-CohFTs, and integrable hierarchies

A Arsie, A Buryak, P Lorenzoni, P Rossi - … in Mathematical Physics, 2021 - Springer
We define the double ramification hierarchy associated to an F-cohomological field theory
and use this construction to prove that the principal hierarchy of any semisimple …

Quadratic double ramification integrals and the noncommutative KdV hierarchy

A Buryak, P Rossi - Bulletin of the London Mathematical …, 2021 - Wiley Online Library
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 …

Semisimple flat F-manifolds in higher genus

A Arsie, A Buryak, P Lorenzoni, P Rossi - … in Mathematical Physics, 2023 - Springer
In this paper, we generalize the Givental theory for Frobenius manifolds and cohomological
field theories to flat F-manifolds and F-cohomological field theories. In particular, we define a …

Stable tree expressions with Omega-classes and Double Ramification cycles

X Blot, D Lewański, P Rossi, S Shadrin - arXiv preprint arXiv:2403.05190, 2024 - arxiv.org
arXiv:2403.05190v1 [math.AG] 8 Mar 2024 Page 1 arXiv:2403.05190v1 [math.AG] 8 Mar
2024 STABLE TREE EXPRESSIONS WITH OMEGA-CLASSES AND DOUBLE …

Moduli spaces of residueless meromorphic differentials and the KP hierarchy

A Buryak, P Rossi, D Zvonkine - arXiv preprint arXiv:2110.01419, 2021 - arxiv.org
We prove that the cohomology classes of the moduli spaces of residueless meromorphic
differentials, ie, the closures, in the moduli space of stable curves, of the loci of smooth …

Riemann–Hilbert–Birkhoff inverse problem for semisimple flat FF‐manifolds and convergence of oriented associativity potentials

G Cotti - Journal of the London Mathematical Society, 2024 - Wiley Online Library
In this paper, we address the problem of classification of quasi‐homogeneous formal power
series providing solutions of the oriented associativity equations. Such a classification is …

Riemannian F-manifolds, bi-flat F-manifolds, and flat pencils of metrics

A Arsie, A Buryak, P Lorenzoni… - International Mathematics …, 2022 - academic.oup.com
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 …

Integrable systems of finite type from F-cohomological field theories without unit

A Buryak, D Gubarevich - Mathematical Physics, Analysis and Geometry, 2023 - Springer
One of many manifestations of a deep relation between the topology of the moduli spaces of
algebraic curves and the theory of integrable systems is a recent construction of Arsie …