Related papers: The Hodge-FVH Correspondence

In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there…

We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric Robinson-Schensted-Knuth correspondence…

We describe a method to compute Hurwitz-Hodge integrals.

Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric…

A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight k-1, its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which…

In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…

A many-particle Hamiltonian is proposed in order to explain the fractional quantum Hall effect (FQHE) for fractional filling factors $\nu < 1$. The solutions of the corresponding Hartree-Fock equations make it possible to discuss the FQHE…

Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with…

Let $(H, \a)$ be a monoidal Hom-Hopf algebra and $(A, \b)$ a right $(H, \a)$-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of $(A, \b)$ in the setting of monoidal Hom-Hopf algebras. Also we…

We define Hodge correlators for a compact Kahler manifold X. They are complex numbers which can be obtained by perturbative series expansion of a certain Feynman integral which we assign to X. We show that they define a functorial real…

The Lewis-Zagier correspondence, which attaches period functions to Maa\ss\ wave forms, is extended to wave forms of higher order, which are higher invariants of the Fuchsian group in question. The key ingredient is an identification of…

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf…

A new expression for solving homogeneous linear ODEs based on a generalization of the Volterra composition was recently introduced. In this work, we extend such an expression, showing that it corresponds to inverting an infinite matrix.…

In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…

We examine affine correspondences of the form g(y)=f(x), for f and g polynomials satisfying deg(g) < deg(f), with the property that every critical point of the correspondence admits at least one finite forward orbit. In the case g(y)=y,…

We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homology, called Hopf--Hochschild (co)homology, can also be…

A new holographic duality named Kerr/CFT correspondence was recently proposed to derive the statistical entropy of four-dimensional extremal Kerr black holes via identifying the quantum states in the near-horizon region with those of…

A convex triangular grid is represented by a planar digraph $G$ embedded in the plane so that (a) each bounded face is surrounded by three edges and forms an equilateral triangle, and (b) the union $\Rscr$ of bounded faces is a convex…

For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…