Vavilov Nikolay Aleksandrovich (Dr. Sc., Professor, St. Petersburg State University) will give a mini-course of lectures at NSU 鈥淩estricted generation of Chevalley groups, and around鈥�. The course consists of 4 lectures, which will be held May 23鈥�26 at 16:20 in auditorium 5239 NSU.
The course will cover the restricted generation of groups of points of algebraic groups over commutative rings, primarily rings of arithmetic type. Will discuss:
- elementary width
- width in switches
- verbal width in general.
We recall the basic definitions, statement of the problem and several classical results on elementary width (Carter, Keller, Tavgen, Morris, etc.) related to the numerical case. And also results on commutator and verbal width in the case of fields and other zero-dimensional rings (around the Ore problem, results of Shalev and students of Lyubotsky, etc.).
After this, it is planned to talk about recent results on the elementary width obtained in the most recent years by Nika, Kunyavsky, Plotkin, the speaker, Trost, Rapinchuk, Suri, Morgan, Lavrenov, and others - in the functional case, for rank 1 and in some other situations, improved grades, etc. - and describe several basic ideas used in their proofs (Tavgen's trick, stabilization, Mennike symbols, etc.). These results are new for SL(n,F_q[t]) and Sp(2l,F_q[t]) .
In addition, results of Stepanov and others on the width of commutators in the case of arbitrary commutative rings and partial results in a similar spirit for more general words will be presented. It is also planned to mention the connection with further problems of this type (congruence problem, etc.) and model theory and to formulate several open problems in this area.
Details and registration 鈥� on the website .
