The paper surveys open problems and questions related to interplay between the theory of
integrable systems with infinitely and finitely many degrees of freedom and Nijenhuis …

The core object of this paper is a pair (L, e) (L,e), where LL is a Nijenhuis operator and ee is
a vector field satisfying a specific Lie derivative condition, that is, L e L= Id L_eL=Id. Our …

We study the family of ordinary differential equations associated to a Dubrovin-Frobenius
manifold along its caustic. Upon just loosing an idempotent at the caustic and under a non …

Given an F-manifold one may construct a dual multiplication (generalizing the idea of an
almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity …

Originated in the context of two-dimensional topological field theories, Frobenius manifolds
lie at the intersection of several areas of mathematics, embracing integrable systems …

F-manifold algebras are focused on the algebraic properties of the tangent sheaf of F-
manifolds. The local classification of 3-dimensional F-manifolds has been given in A …

Dubrovin-Frobenius manifolds were invented by Boris Dubrovin to geometrize the study of
certain 2D Topological Field Theories ([11],[12]). The primary free energy F of a family of …