Related papers: Lectures on Symmetric Tensor Categories
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
Traced monoidal categories are used to model processes that can feed their outputs back to their own inputs, abstracting iteration. The category of finite dimensional Hilbert spaces with the direct sum tensor is not traced. But…
Using the theory of measurable categories developped by Yetter in work in preparation, we provide a notion of representations of 2-groups more well-suited to physically and geometrically interesting examples than that proposed in…
Tensor models and tensor field theories admit a $1/N$ expansion and a melonic large $N$ limit which is simpler than the planar limit of random matrices and richer than the large $N$ limit of vector models. They provide examples of…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called "second" variational principle, where the argument of the Lagrangian is a closed…
These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of…
We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with Semi-Dihedral groups $SD_{8n}$. The dimensions of these symmetry classes of tensors are also computed.
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
This is the extended write-up of a series of lectures on the duality between the Sine-Gordon model and the Thirring model. Prepared for the London Theory Institute (LonTI) - Fall 2022: a PhD-level mini-course, with exercises and a guide to…
The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements…
It is shown in this article that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse…
The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…
In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are…
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…
We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.
These notes accompany an introductory lecture course on the twistor approach to supersymmetric gauge theories aimed at early-stage PhD students. It was held by the author at the University of Cambridge during the Michaelmas term in 2009.…
This is a series of lecture notes explaining topos theory and its application in physics.