Date & Time: Wednesday, May 11, 2016, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: Prof. Maneesh Thakur, Stat-Math Unit, ISI Delhi
Title: R-triviality of some (exceptional) algebraic groups
Abstract: Let F be a field having at least four elements. Then it is a classical result that the group SL(n,F) of n by n matrices of determinant 1 with F-entries, is generated by unipotent matrices (i.e. those which have all eigenvalues equal to 1) and that SL(n,F) is simple modulo its center. Let G be a simple and simply connected group over F (e.g. G=SL(n) ). Kneser-Tits conjecture predicts that if G(F) contains non-trivial unipotents, then G(F) is simple modulo its center. The conjecture is well known to be false. The obstruction to validity of the conjecture lies in the Whitehead group of G. Hence one is interested in computing this obstruction. If this obstruction is trivial, then G(F) is simple modulo its center, providing interesting examples of (abstract) simple groups. We will discuss two geometric notions for algebraic groups, called R-equivalence (due to Manin), and retract rationality and mention a link with Whitehead groups and finally report on some recent work on the problem.