Related papers: Excursions in Group Theory
We introduce a model, based on the Evolutionary Game Theory, for studying the dynamics of group formation. The latter constitutes a relevant phenomenon observed in different animal species, whose individuals tend to cluster together forming…
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each…
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these…
This paper is an appendix to the paper "Random walks on free products of cyclic groups" by J.Mairesse and F.Math\'eus. It contains the details of the computations and the proofs of the results concerning the examples treated there.
These notes are a self-contained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in…
We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…
We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.
Lecture notes on selected topics in the theory of gravitation.
Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.
We review recent developments in the theory of Thompson group representations related to knot theory.
Physical properties of matter are tightly related with the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
This is a collection of questions that I am considering submitting to the next edition of the Kourovka Notebook of open questions in group theory. Most are questions I raised in papers between 1981 and the present; a few are new. I welcome…
The notion of travel groupoids was introduced by L. Nebesk\'y in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set $V$ and a binary operation $*$ on $V$ satisfying two axioms. For a travel groupoid, we…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).