Expander families are sequences of finite, highly connected, sparse graphs with an increasing number of vertices. They have lead to breakthroughs in various areas of mathematics and have become indispensable in theoretical computer science. Originally, the existence of expander families was shown by probabilistic methods (random graphs), but nowadays, several explicit constructions relying on different methods are known. This course will give an introduction to expander families, some of their fascinating geometric features, and some applications.
This course will be held in English. The target audience of this course is PhD students and advanced master students. The topics covered will partly depend on the interests of the audience.
Participants are expected to have a bachelor in mathematics (including basic functional analysis) and some additional mathematical maturity. This course involves methods from different areas of mathematics (functional analysis, combinatorics, probability theory, group theory, geometry, ...). Specific preliminaries can be recalled if necessary.