Zlil Sela and Alex Lubotzky "Model theory of groups"

In the first part of the course we will present some of the main results in the theory of free,

hyperbolic and related groups, many of which appear as lattices in rank one simple Lie groups

We will present some of the main objects that are used in studying the theory of these groups,

and at least sketch the proofs of some of the main theorems.

In the second part of the course, we will talk about the model theory of lattices in high rank simple Lie groups.

The latter behave very differently from the first. These lattices are all arithmetic ( by Margulis seminal work)

and their model theory is related to other properties, like super-rigidity, bounded generations, the congruence

subgroup problem and more.

All needed material will be explained.

In the first part of the course we will present some of the main results in the theory of free,

hyperbolic and related groups, many of which appear as lattices in rank one simple Lie groups

We will present some of the main objects that are used in studying the theory of these groups,

and at least sketch the proofs of some of the main theorems.

In the second part of the course, we will talk about the model theory of lattices in high rank simple Lie groups.

The latter behave very differently from the first. These lattices are all arithmetic ( by Margulis seminal work)

and their model theory is related to other properties, like super-rigidity, bounded generations, the congruence

subgroup problem and more.

All needed material will be explained.

## Date:

Sunday, 31 March, 2019 - 11:00 to 13:00

Repeats every week every Sunday until Sat Jun 29 2019 except Sun Apr 21 2019