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
Fundamental Groups and Dendricity
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...
Return Groups of Eventually Dendric Shifts
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 ...
Aspects of Abstract Regular Polytopes and The Combinatorics of Coxeter Groups
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 exact meaning of the angular-momentum and spin operators in quantum mechanics
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...
A workshop on the epistemology and didactics of mathematical structuralism
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...
Groups Acting on Products of Trees
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...
Topics in Particle Physics, Quantum Field Theory, and Cosmology
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...
Symmetry Analysis of Orbitals in a Plane Wave Basis : A Study on Molecules and Defects in Solids / Symmetrianalys av Orb...
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...
A proposal to get some common-sense intuition for the paradox of the double-slit experiment
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...
