Related papers: Lectures on Symmetric Tensor Categories
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
In this second installment of SETI in 20xx, we very briefly and subjectively review developments in SETI in 2021. Our primary focus is 98 papers and books published or made public in 2021, which we sort into six broad categories: results…
This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement…
The piezoelectricity law is a constitutive model that describes how mechanical andelectric fields are coupled within a material. In its linear formulation this law comprises threeconstitutive tensors of increasing order: the second order…
These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
In this paper, we introduce the notion of developments of curves with respect to symmetric tensors and use it to prove the existence of isometric immersions into a general ambient space with prescribed second fundamental form. Our method…
This is a review of the theoretical aspects of the supersymmetric extension of the Standard Model of particle physics, extracted from Chapter 87 of the 2026 Review of Particle Physics, F. Takahashi et al. (Particle Data Group), Int. J. Mod.…
We develop a notion of iterated monoidal category and show that this notion corresponds in a precise way to the notion of iterated loop space. Specifically the group completion of the nerve of such a category is an iterated loop space and…
This is an overview of the basics of inverse semigroup theory written for the Workshop on Semigroups and Categories held at the University of Ottawa in 2010.
In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative…
This paper establishes sharp concentration inequalities for simple random tensors. Our theory unveils a phenomenon that arises only for asymmetric tensors of order $p \ge 3:$ when the effective ranks of the covariances of the component…
This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems. Exciting recent developments include new methods involving…
We continue to develop the theory of separable higher categories, including center functors, higher centralizers, modular extensions and group theoretical higher fusion categories. Moreover, we outline a theory of orthogonal higher…
Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been…
In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$…
The article provides a review of the publications on the current trends and developments in Dempster-Shafer theory and its different applications in science, engineering, and technologies. The review took account of the following provisions…
In this article, we will investigate several new configurations in Ramsey Theory, using the $\ostar_{l,k}$-operation on the set of integers, recently introduced in \cite{key-4}. This operation is useful to study symmetric structures in the…
These notes attempt to give a short survey of the approach to support theory and the study of lattices of triangulated subcategories through the machinery of tensor triangular geometry. One main aim is to introduce the material necessary to…
In this thesis my papers hep-th/0104190, hep-th/0310214, hep-th/0405072 and hep-th/0406065 are put into context. The thesis is mainly focused on noncommutative field theory and string theory, so results in the papers that are not related to…