Quadratic forms over Grassmannians
St. Edmund's College, Cambridge, U.K.
I will recall the construction of the Witt group of a field, which is an invariant to classify quadratic forms over this field, going back to Witt (1937). Then, I will explain how this construction generalizes to an abstract setting, which enables us to define Witt groups of varieties instead of just fields. After explaining the usual properties of these Witt groups of varieties, I will explain how to compute the Witt groups of the classical Grassmann varieties (joint work with Paul Balmer).