NSCPHD1094 Introduction to Coxeter groups and buildings

The aim of the course is to provide students with an elementary introduction to Coxeter groups and buildings. Coxeter groups form an interesting and rich class of groups that are important throughout many areas of mathematics such as geometric group theory, Lie theory, representation theory and topology. A building is a certain geometric object that can be associated to a Coxeter group. Buildings were initially introduced to study groups of Lie type, but are now used in many other places and studied in their own right.

In part 1 of the course I will deal with Coxeter groups. I will start from the very basics and give full details of proofs in class. The basic reference for this part is Mike Davis his book 'The geometry and topology of Coxeter groups'.

In part 2 we will talk about building. This part will rely heavily on what we have learned in part 1. Depending on what the attending student want, I can again be very rigorious here, but not get very far in the theory. Or we can focus more on applications of buildings in several areas of math, and skip some or many details and proofs. The basic reference for this part will be the book by Peter Abramenko and Kenneth Brown called 'Buildings, theory and applications'.