Department of Mathematics
Mathematics Seminar Series - Spring 2011
Wednesday,
March 30, 2011
2:30pm - 4:00pm, M-2-116
2:30pm - 4:00pm, M-2-116
Alex Suciu
Northeastern UniversityOn the Johnson filtration of the automorphism group of a free group
Abstract:
Given any group G, the commutator defines
a descending filtration on G, known as the lower central
series. The automorphism group, Aut(G), supports
yet another filtration: an automorphism belongs
to the k-th term of this ``Johnson filtration'' if
it has the same k-jet as the identity, with respect
to the lower central series of G.
In this talk, I will discuss the Johnson filtration
of the automorphism group of a finitely generated
free group F_n, with emphasis on the homological
finiteness properties of the first few terms in
the filtration. The automorphism group of the
abelianization, GL_n(Z), and the representation
theory of the corresponding Lie algebra, gl_n(C),
will play an important role in the story.
This is joint work with Stefan Papadima (arXiv:1011.5292).
The presentations cover a large variety of topics and are intended for a general math audience. The seminar is organized by Prof. Eduardo Gonzalez and we usually meet Wednesday afternoons, from 2:30 pm to 4:00 pm.
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