Abstract:

The questions of which kind of groups are linear and what algebraic properties linear groups have have been studied a lot. In the 60's Lazard characterized linear pro-p groups over the p-adics. Lubotzky and Mann extended his work and gave additional useful characterizations. Recently Pink was able to reduce the study of compact groups over local fields of positive characteristic to open subgroups of algebraic groups over local fields.

I will present results on representations of free pro-p groups and will give some algebraic properties of linear pro-p groups. Tools from various areas of mathematics were applied for these results, such as the theory of algebraic groups, Lie methods, and the probabilistic method. I will try to shed light on how they were used.

I will explain in the talk what a pro-p group is and will give several examples.

Coffee, Cookies, Company at the faculty lounge at 3:30.