Detailed information about the course
Title  Graduate lectures in mathematics 
Dates  February 22  Mai 31, 2018 
Responsable de l'activité  Sebastian Baader 
Organizer(s)  
Speakers  Alexander Kolpakov, Prof. Dr., Université de Neuchâtel, Alessandro Sisto, Prof. Dr., ETH Zurich 
Description  Thursday 14.1515.45 Prof. Dr. Alexander Kolpakov: Reflection Groups and Coxeter Groups Thursday 16.001730 Prof. Dr. Alessandro Sisto: Geometric Group Theory 
Location 
University of Bern, room B13 ExWi, Sidlerstrasse 5, Bern 
Information  Alexander Kolpakov: Reflection groups and Coxeter groups Summary: This course is devoted to the study of very handson and simultaneously complicated and fascinating objects: symmetry groups generated by reflections. Such groups are abundant in nature, and represent symmetries of many mathematical and natural objects, be them Platonic solids or biological and chemical structures, such as cells, microorganisms, or molecules. We shall starts with a geometric exploration of reflection groups, their root systems and diagrams, as well as associated geometric complexes (Coxeter complex and Davis complex). We shall continue on classifying finite groups. Then we shall generalise this notion gradually, and see how our techniques evolve (and we will be able to treat even the most general case very similarly to what we started with: finite reflection groups). Finally, we will discuss abstract Coxeter groups, their presentations and representations, and associated geometric structures, such as geometric spaces (spherical, Euclidean and hyperbolic), and geometry of their Coxeter and Davis complexes (including an excursion into CAT spaces). As well, we shall devoted some time to the classification of Coxeter groups of a very widespread and important kind: hyperbolic Coxeter groups (and see their connection with Gromov's wordhyperbolic groups). This course will partially complement "Geometric Group Theory", as well as "Geometric Group Theory" will help understanding some of its more advanced chapters. Alessandro Sisto: Geometric Group Theory Summary: Geometric group theory is the study of groups (usually infinite, finitely generated ones) using geometric methods. I will first of all introduce a key object in geometric group theory, namely the Cayley graph, which is a metric space associated to a group and a finite generating set, and I will explain its relation to nice isometric actions of the group itself (through the notion of quasiisometry and the MilnorSvarc Lemma).

Registration  under: 
Places  15 
Deadline for registration  20.02.2018 