Quadratic forms and Bott periodicity

Abstract:

Bott periodicity has various formulations in homotopy theory. We present here an  interpretation in terms or quadratic forms and symplectic structures. This can be translated in the  framework of Quillen's algebraic K-theory for classical groups. We also announce the recent  proof of two classical conjectures: the Quillen-Lichtenbaum conjecture in hermitian K-theory  and the homotopy limit problem for the orthogonal group. We conclude by some examples of  computations.

Аннотация лекции