Abstract homomorphisms of algebraic groups and applications

Joint IAS/Princeton University Number Theory Seminar
Topic:Abstract homomorphisms of algebraic groups and applications
Speaker:Igor Rapinchuk
Affiliation:Michigan State University
Date:Tuesday, February 13
Time/Room:4:45pm - 5:45pm/Simonyi Hall 101
Video Link:https://video.ias.edu/puias/2018/0213-IgorRapinchuk

I will discuss several results on abstract homomorphisms between the groups of rational points of algebraic groups. The main focus will be on a conjecture of Borel and Tits formulated in their landmark 1973 paper.
 
Our results settle this conjecture in several cases; the proofs make use of the notion of an algebraic ring. I will mention several applications to character varieties of finitely generated groups and representations of some non-arithmetic groups.