Analysis and Geometry on Groups
following classical problems in group theory will be discussed:
- Siegel problem: finite generation of lattices.
- Margulis construction: expander graphs.
- Atiyah invariants: L2 Betti numbers.
- Gromov problem: non-uniform exponential growth.
- Burnside groups: infinite, finitely generated torsion groups.
- Day class: exotic amenable groups.
Along presenting solutions to these problems we will introduce the following
- Amenability and property (T).
- Random groups and graphs.
- Groups generated by automata.
- L2 invariants of groups and manifolds.
- Random walks on groups and graphs.