Related papers: The Tensorial Connections
We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…
Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
Computational materials design often profits from the fact that some complicated contributions are not calculated for the real material, but replaced by results of models. We turn this approximation into a very general and in principle…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
The work starts a series of papers on topological radicals and their applications. Among other results we present a theory of radicals related to the joint tensor radius.
We review the twistorial structures by providing a setting under which the corresponding (differential) geometry can be described, by involving the $\rho$-connections. This applies, for example, to give new proofs of the existence of the…
Prompted by an example related to the tensor algebra, we introduce and investigate a stronger version of the notion of separable functor that we call heavily separable. We test this notion on several functors traditionally connected to the…
We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…
In this talk I review recent advances on the structure of the meson and baryon resonances which can be dynamically generated from the interaction of mesons or mesons and baryons. Particular emphasis is put on results involving vector…
In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of…
The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
This paper extends the univariate Theory of Connections, introduced in (Mortari,2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface,…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…
This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.