Related papers: Lecture notes on CAT(0) cube complexes

These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.

Quasi-median graphs have been introduced by Mulder in 1980 as a generalisation of median graphs, known in geometric group theory to naturally coincide with the class of CAT(0) cube complexes. In his PhD thesis, the author showed that…

In this paper, we study the geometry of cone-offs of CAT(0) cube complexes over a family of combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives a direct cubical proof of the…

In this short note, we show that a group acting geometrically on a CAT(0) cube complex with virtually abelian hyperplane-stabilisers must decompose virtually as a free product of free abelian groups and surface groups.

This is the first of three PiTP lectures on complexity and its role in black hole physics.

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…

The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…

This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…

These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.

This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different…

In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…

These lecture notes from a first course in algebraic topology use the fundamental group and orbit categories to classify covering spaces.

This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…

We bound the size of $d$-dimensional cubulations of finitely presented groups. We apply this bound to obtain acylindrical accessibility for actions on CAT(0) cube complexes and bounds on curves on surfaces.

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…

These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.

The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…

These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced…