Motivic Galois groups and applications
Institut fur Mathematik, Universitat Zurich.
The "conjectural" motivic Galois group is a generalization of the Galois group that we know from the theory of eld extensions. It is expected to "classify" all cohomological information over a eld in the similar way Galois groups classify all algebraic eld extensions or fundamental groups (Seall coverings. In my talk we will rst explore the construction of M. Nori of motivic Galois group and state a conjecture of Kontsevich and Zagier (called the Period conjecture). Then we will explore a new construction of motivic Galois group by J. Ayoub. This new construction and the theory related to it is used by Ayoub to solve a version of Kontsevich and Zagier's conjecture. These two versions are same provided the motivic Galois groups are canonically isomorphic. If time permits we will see that these two Galois groups are indeed isomorphic (work in progress with Martin Gallauer Alves de Souza).