Schedule

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Prerequisite

Essential prerequisites: undergraduate group theory and linear algebra. Desirable prerequisites (introductory) topology and representation theory.

Introduction

Braid groups are special types of groups which appear in many areas of pure and applied mathematics. We will mainly focus on the family of "standard" braid groups (Artin braid groups), which are closely connected to the family of symmetric groups. They can be presented by generators & relations but also have more intuitive topological reailizations. There are natural connections for instance with Coxeter groups, reflection groups and Iwahori-Hecke algebras, with semisimple Lie algebras, with knot theory and with mathematical physics. We will explore many of these connections and discuss some important representations. The course is aimed at postgraduate students in mathematics and related disciplines.

Reference

Kassel & Turaev, Braid groups, Graduate Texts in Mathematics 247, Springer.

Record

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Lecturer Intro

Dr. Bart Vlaar has joined BIMSA in September 2022 as an Associate Professor. His research interests are in algebra and representation theory and applications in mathematical physics. He obtained a PhD in Mathematics from the University of Glasgow. Previously, he has held postdoctoral positions in Amsterdam, Nottingham, York and Heriot-Watt University. Before coming to BIMSA he visited the Max Planck Institute of Mathematics in Bonn.