School of Mathematics
This is a series of 3 talks on the topology of Stein manifolds, based on work of Eliashberg since the early 1990ies. More specifically, I wish to explain to what extent Stein structures are flexible, i.e. obey an h-principle. After providing some general background on Stein manifolds, the first talk will focus on the construction of plurisubharmonic functions with specific properties. Using these, I will in the second talk present the proof of Eliashberg's existence theorem for Stein structures.
In the first part, we will discuss two options for using groups to construct expander graphs (Cayley graphs and Schreier diagrams). Specifically, we will see how to construct monotone expanders in this way. As in recent works (e.g. of Bourgain and Gamburd), we will see that the proof consists of 3 different steps. We will shortly discuss these 3 steps.