Lecture 1: Hyperplane Arrangements: Combinatorics and Cohomology 
(speaker: Clement Dupont)

Abstract: This course will introduce the combinatorial study of hyperplane arrangements (posets, matroids) and present topological and geometric invariants of arrangements that are combinatorially determined.

 Lecture 2: Hyperplane Arrangements: Fundamental Groups
(speaker: Ivan Marin)

 Abstract: This course will focus on the fundamental group of the complement of a hyperplane arrangement, and establish the necessary topological preliminaries : fundamental group, homology, cohomology. It will also present the case of reflection arrangements, whose study yields to the (generalized) braid groups and their presentations.


Lecture 3: Introduction to Homotopy Theory
(speaker: Nguyen Viet Dung)

Abstract: The course offers an introduction to elementary homotopy theory centered around the fundamental group of a topological space and covering spaces.

The course will start with a reminder about the fundamental knowledge of general topology. Next, the course will introduce the homotopy relation on maps, define the (higher) homotopy groups of a space. The course put an emphasis on the fundamental group and prove some basic properties about them as well as compte the fundamental group for some familiar spaces, using the Van Kampen theorem. Finally, the course introduce the covering spaces and the lifting theorem in connection with the action of the fundamental group.


Lecture 4: Representation Theory
(speaker: Nguyen Bich Van)

 Abstract: The main aim of the course will be to understand the classification of finite reflection groups. The course will begin with an introduction to theory of representation. Then the course will focus on finite reflection groups. We will introduce the notion of root systems, Coxeter graphs and Coxeter groups, classification of Coxeter groups. Some combinatorial aspects will also be covered.