Speaker: Laurent Bartholdi

Abstract:
A construction by Magnus associates a Lie algebra to a discrete group, by considering the associated graded to a descending filtration of the group, e.g. by its lower central series.
The automorphism group of a free group has a very intricate structure, but one may hope that its associated Lie algebra is more manageable to study. It is naturally a subalgebra of the algebra of "free differential operators", and I will explain which part of that algebra is associated with the automorphism group of a free group.