Talk abstracts

Speaker: Kasia Janikiewicz (UC Santa Cruz)

Title: Artin groups and their geometric representations

Abstract: Artin groups are a family of groups generalizing braid groups and are closely related to Coxeter groups. They can be defined using simple looking group presentations, but in general many of their basic properties are still unknown. In this series of talks, I will start with reviewing various definitions of Artin groups and discussing some examples. I will then give an overview of various approaches to study of Artin groups, using combinatorial and geometric tools. A geometric representation of an Artin group is a representation in a mapping class group. While some Artin groups do not admit faithful geometric representations, representations that are not faithful can be still useful for understanding the structure of Artin groups. I will discuss some such representations and their applications. 

Introductory speakers:

• Jagerynn Verano -- Introduction to Artin groups

• Zihao Liu -- Introduction to general-type Artin groups

• Ethan Dlugie -- The Burau representation and shapes of polyhedra