Coarse Geometry and $C^*$ algebras

Title 1,2: Random groups: basic techniques for hyperbolicity and phase transitions
In the first talk we will give the main steps of the proof that hyperbolic groups are generic in the density model, and that depending upon the density of the presentation a transition phase occurs between infinite and trivial groups. In the second lecture we will show that hyperbolicity is stable for groups, with a critical density depending on spectral properties of hyperbolic groups.

Title 3: Random groups: construction of Cayley graphs with expanders
In this third talk we will give the main ideas of Gromov's construction of a group containing expanders, and describe how random groups can be used to get Cayley graphs of prescribed shapes.

Topics in geometric group theory

Topics in analysis and geometry on groups
lecture 1: Property T
lecture 2: Random groups and automata groups
lecture 3: L^2 Betti numbers