August 17 – 28, 2015
The algebraic theory of quadratic forms was founded by Witt in 1936. Voevodsky’s proof of the Milnor’s conjecture, in the 90’s, led to a spectacular renewed theory, where motivic methods play a fundamental rôle. This result, which is a particular case of Bloch-Kato’s conjecture, also partially answers the classification question for quadratic forms over an arbitrary field.
From the point of view of algebraic groups, the theory of algebras with involution is a natural extension of quadratic form theory. Even though cohomological invariants of quadratic forms do not always extend to involutions, their study led to important progress on classification of involutions, especially in small dimension and orthogonal and symplectic type, as was shown in some recent papers. Our project is to study cohomological invariants of unitary involutions.
Demba Barry (Université de Bamako)