**Jean Fasel**

Ecole Polytechnique Federale de Lausanne, Switzerl

September 3, 2010

**Grothendieck-Witt groups and projective modules**:
We will present new developments in the theory of Grothendieck-Witt groups (aka Hermitian K-theory), and then give some nice applications. In particular, we will prove Suslin's conjecture that stably free modules of rank d-1 over a smooth affine algebra of dimension d over an algebraically closed field are free.