The aim of this work is to study risk measures generated by distortion functions in a dynamic
discrete time setup and to investigate the corresponding dynamic coherent acceptability …

In this paper we present a new construction of a hamiltonian hierarchy associated to a
cohomological field theory. We conjecture that in the semisimple case our hierarchy is …

For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of
Hamiltonian partial differential equations. In the particular case of quantum cohomology the …

We define a hierarchy of Hamiltonian PDEs associated to an arbitrary tau-function in the
semi-simple orbit of the Givental group action on genus expansions of Frobenius manifolds …

For any semisimple Frobenius manifold, we prove that a tau-symmetric bihamiltonian
deformation of its Principal Hierarchy admits an infinite family of linearizable Virasoro …

In 1991, Witten [41] proposed a remarkable conjecture relating the intersection theory of the
Deligne–Mumford moduli space Mg, k to the Kortweg-de Vries (KdV) hierarchy. The …

In this paper we continue the study of the double ramification hierarchy of Buryak (Commun
Math Phys 336 (3): 1085–1107, 2015). After showing that the DR hierarchy satisfies tau …

We show that the equivalence classes of deformations of localizable semisimple Poisson
pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain …

Let M be an n-dimensional Frobenius manifold. Fix κ∈{1,⋯, n}. Assuming certain invertibility,
Dubrovin introduced the Legendre-type transformation S κ, which transforms M to an n …

In this paper we study various aspects of the double ramification (DR) hierarchy, introduced
by the 1st author, and its quantization. We extend the notion of tau-symmetry to quantum …