Minicourse on
Zelmanov characteristic 0 theorem and the Restricted Burnside Problem

The minicourse is offered by our colleague Christian d'Elbée. The notes of the course are available here; the recordings of the lectures are available here.

Title: Zelmanov characteristic 0 theorem and the Restricted Burnside Problem.

Abstract: The course will present the proof of Zelmanov "characteristic 0" theorem: every n-Engel Lie algebra over a field of characteristic 0 is nilpotent. The proof of this wonderful result involves the theory of varieties of Lie algebras, gradation on Lie algebras, and representation of symmetric groups. Nonetheless, the proof consists of a rather intricate direct computation. The connection with the Restricted Burnside Problem will be established, and we will see that this result yields an "asymptotic" solution of the RBP for groups of prime exponent.