## Représentations de réflexion de groupes de Coxeter Deuxième partie: outils pour des exemples

This part is made of three sections. In the first section we study the family of polynomials whose roots are 4cos2 kπ, (n \geqslant 3,1 \leqslant k

This part is made of three sections. In the first section we study the family of polynomials whose roots are 4cos2 kπ, (n \geqslant 3,1 \leqslant k

The aim of the poster is to showcase the interplay between group theory, algebraic topology and combinatorics on words. A result that allows to display this is the return theorem by Berté et al. in 2015. The poster will contain an introduction to fundamental groups of graphs, dendric words as well as a new result concerning return groups of eventua...

Since 2015, dendric shifts (a generalisation of Sturmian words) have been widely studied. One of the results concerning these shift spaces is the return theorem. It describes the groups generated by the return words of a dendric shift. The proof uses the fundamental group of the Rauzy graph of the shift space. Later, eventually dendric shifts were ...

In this thesis, we examine abstract regular polytopes and some combinatorics of Coxeter groups. For abstract regular polytopes, we define the notion of when such polytopes are unravelled. We then go on to examine and catalogue examples of these abstract regular polytopes. We construct four different non-trivial infinite families and analyse some sm...

The theory of angular momentum and spin in quantum mechanics seems to defy common-sense intuition.We render the theory intelligible again by pointing out that this apparent impenetrability merely stems from an {\em undue} parallel interpretation of the algebraic expressions for the angular-momentum and spin operators in the group representation the...

This workshop was dedicated to a discussion of epistemological and didactic aspects of mathematical structuralism with a focus on Abstract Algebra, in particular Group Theory. The participants worked on a corpus of documents comprising excerpts of the Bourbaki Manifesto “the architecture of mathematics” and the transcript of a discussion thread fro...

In this thesis, we explore many aspects of groups acting on trees and on products of trees. These ideas are central to the field of geometric group theory, the study of infinite groups by their large-scale behavior. Many of our techniques are algebraic and arithmetic in nature. Most of this work is motivated by the following question:\begin{ques} I...

Our understanding of particles physics derives, in large part, from our ability to do perturbative calculations by expanding around small coupling. This Feynman diagrammatic approach has been incredibly successful in providing physicists a means to approximate physical observables. However, there are many scenarios where a perturbative approach eit...

Modeling and analysing materials with theoretical tools is of great use when finding new systems for applications, for example, semiconductors with point defects can be used for quantum applications, like single photon emitters. One important aspect to consider symmetry, which can yield useful information about the properties of a system. To perfor...

We argue that the double-slit experiment can be understood much better by considering it as an experiment wherebyone uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons.We also show that the concept of undecidability (like e.g. occurs in G\"odel's theorem) can be used in an intuit...