**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.