**Anand Sawant**

University of Munich, Germany

September 14, 2017

**Central extensions and A^1-fundamental groups**:
Classical results of Matsumoto and Suslin describe the universal central extension of the group of rational points of a split, semisimple, simply connected algebraic group. These results were later extended by Brylinski and Deligne, who determined the category of central extensions of a reductive group by the second K-theory sheaf K_2. We will discuss how these classical results can be uniformly explained and generalized using the so-called motivic or A^1-fundamental group of a reductive algebraic group and describe some interesting consequences. The talk is based on joint work in progress with Fabien Morel.