Related papers: Curvature invariant on noncommutative polyballs

Here we study the space of real hyperbolic plane curves that are invariant under actions of the cyclic and dihedral groups and show they have determinantal representations that certify this invariance. We show an analogue of Nuij's theorem…

In this paper, we extend the Brown-Halmos theorems to the Fock space and investigate the range of the Berezin transform. We observe that there are non-pluriharmonic functions $u$ that can be written as a finite sum…

A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…

Inspired by piecewise polynomiality results of double Hurwitz numbers, Ardila and Brugall\'e introduced an enumerative problem which they call double Gromov--Witten invariants of Hirzebruch surfaces. These invariants serve as a…

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.

This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on…

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…

The spin-base invariant formalism of Dirac fermions in curved space maintains the essential symmetries of general covariance as well as similarity transformations of the Clifford algebra. We emphasize the advantages of the spin-base…

The main result of this paper is the statement that the Hodge theoretic Donaldson-Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure…

We construct a new invariant-the trunkenness-for volume-perserving vector fields on S^3 up to volume-preserving diffeomorphism. We prove that the trunkenness is independent from the helicity and that it is the limit of a knot invariant…

Our aim is to study invariant hypersurfaces immersed in the Euclidean space $\mathbb{R}^{n+1}$, whose mean curvature is given as a linear function in the unit sphere $\mathbb{S}^n$ depending on its Gauss map. These hypersurfaces are closely…

In this paper we initiate the study of composition operators on the noncommutative Hardy space $H^2_{\bf ball}$. Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness,…

In this article, we explore the following statement made by V. Ginzburg and T. Schedler in [Selecta Math. (N.S.) 16 (2010), no. 4, 673-730]: "an adequate framework for doing noncommutative differential geometry is provided by the notion of…

It is well known that the Jacobi operators completely determine the curvature tensor. The question of existence of a curvature tensor for given Jacobi operators naturally arises, which is considered and solved in the previous work.…

We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This allows us to completely classify topological isomorphism…

We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional…

This paper deals with the question of prescribing the Gaussian curvature on a disk and the geodesic curvature of its boundary by means of a conformal deformation of the metric. We restrict ourselves to a symmetric setting in which the…

We extend the framework of K-stability (Tian, Donaldson) to more general algebro-geometric setting, such as partial desingularisations of (fixed) singularities, (not necessarily flat) families over higher dimensional base and the classical…

We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct the associated analytic torsion form T. If Z is a smooth closed aspherical manifold, we show that T gives…

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…