Related papers: A (very short) introduction to buildings

In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…

We introduce L-presentations: group presentations given by a generating set, a set of relations and a set of substitution rules on the generating set producing more relations. We first study in full generality the structure of finitely…

The presence of infinitesimals is traced back to some of the most general algebraic structures, namely, semigroups, and in fact, magmas, [1], in which none of the structures of linear order, field, or the Archimedean property need to be…

We look at simple groups associated primarily with the general theory of Moufang buildings, and to analyze their relation to stability theory in the model theoretic sense. As it becomes quite technical in the details, a lengthy introduction…

These lectures on the combinatorics and geometry of 0/1-polytopes are meant as an \emph{introduction} and \emph{invitation}. Rather than heading for an extensive survey on 0/1-polytopes I present some interesting aspects of these objects;…

We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…

The aim of this paper is two-fold. First, the study of $C_{12}$-structure (called by us corner structure) is extended to the general case without any condition, unlike our previous papers (see, \cite{BB, BG2, BG, BBB}). Second, starting…

General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…

The present thesis studies structural properties of non-crossing partitions associated to finite Coxeter groups from both algebraic and geometric perspectives. On the one hand, non-crossing partitions are lattices, and on the other hand, we…

These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…

For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…

This book provides a gentle introduction to the study of arithmetic subgroups of semisimple Lie groups. This means that the goal is to understand the group SL(n,Z) and certain of its subgroups. Among the major results discussed in the later…

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…

Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…

Definability is a key notion in the theory of Grothendieck fibrations that characterises when an external property of objects can be accessed from within the internal logic of the base of a fibration. In this paper we consider a…

Student-to-student interactions are foundational to many active learning environments, but are most often studied using qualitative methods. Network analysis tools provide a quantitative complement to this picture, allowing researchers to…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…

Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…

This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…