The lattices in semisimple Lie groups form a very interesting class of groups, which play an important role in geometry, number theory, representation theory, group theory, and model theory. The talk will be an introduction to a series of few talks that will touch on several aspects of these groups.

The current talk will survey various aspects of the congruence subgroup problem and its connection to some boundedness properties of these groups. We will see how these properties ( and related open problems about these groups) are connected to some major problems in modern group theory, like: are all groups sofic? are all hyperbolic groups residually finite?

This will be the opening lecture of a seminar that will meet every Wednesday 11:00 AM-12:15 PM (Toronto time)

The seminar will be hybrid and can be watched live from any place.

We will spend the last 10 minutes or so discussing which topics to study at the continuation of the seminar. Suggestions are welcome (and can also be sent to alex.lubotzky@mail.huji.ac.il).