Yann Ollivier
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.