**Date & Time:** Wednesday, August 12, 2015, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** Anand Sawant, Ludwig Maximilians Universität

**Title:** Rationality questions for algebraic groups and homotopy theory of algebraic varieties

**Abstract:** The notion of R-equivalence, introduced by Manin in the 1970’s, has been very useful in the study of rationality properties of algebraic groups. We will begin with a brief introduction to R-equivalence and discuss some open questions. In the 1990's, Morel and Voevodsky developed a (motivic) homotopy theory for algebraic varieties in which the affine line plays the role of the unit interval. Classical results about R-equivalence combined with recent works in motivic homotopy theory allow one to relate R-equivalence with A1-connectivity in certain algebraic groups. We will give an overview of some recent results in this direction, without going into technical details.