We will discuss a conjecture stating that given a finitely generated field K equipped with a divisorial set of valuations V, an absolutely almost simple algebraic K-group G has only finitely many...
A criterion for strong approximation in algebraic groups was obtained by V. P. Platonov in characteristic zero, and by G. A. Margulis and G. Prasad in positive characteristic. It follows from this...
After surveying some important consequences of the property of bounded generation (BG) dealing with SS-rigidity, the congruence subgroup problem, etc., we will focus on examples of boundedly generated...
A group is said to have bounded generation (BG) if it is a finite product of cyclic subgroups. We will survey the known examples of groups with (BG) and their properties. We will then report on a...
Abstract. After presenting some generalities on the congruence subgroup problem, I will focus on Prasad's work that completely resolved the problem of computation of the metaplectic kernel and also...
Abstract. The famous theorem of Amitsur characterizes finite-dimensional central division algebras over a given field that have the same splitting fields, including infinite-dimensional ones. The...
Abstract. This talk is a progress report on our worked focused on a new form of rigidity that we call eigenvalue rigidity. The latter is based on the notion of weak commensurability of Zariski-dense...
Abstract. The goal of this lecture series is to present the techniques for analyzing arithmetic and general Zariski-dense subgroups of algebraic groups that were developed in a joint work with Gopal...