Expanders and their applications (Summer semester 2020)
Please register for the Learnweb course.
For the time being, this course is offered as an online course. All information, course material and literature will be made available through Learnweb. The target audience is master students and PhD students.
Tim de Laat
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 gives an introduction to expander families, some of their fascinating geometric features, and some applications. The topics covered 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 will be recalled if necessary.