Colloquium
Speaker: Alex Suciu (Northeastern University)
"Automorphism groups, Lie algebras, and resonance varieties"
Time: 15:30
Room: MC 108
The automorphism group of a group $G$
comes endowed with a natural 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, and that of the mapping
class group of a surface, with emphasis on the homological
finiteness properties of the first few terms in these filtrations.
A key ingredient in this approach is a rather surprising
relationship between the classical representation theory
of a complex, semisimple Lie algebra $\mathfrak{g}$
and the resonance varieties $R(V,K)\subset V^*$ attached
to irreducible $\mathfrak{g}$-modules $V$ and submodules
$K\subset V\wedge V$. In the case when $\mathfrak{g}=
\mathfrak{sl}_2(\mathbb{C})$, this relationship sheds new
light on certain modules studied by Weyman and Eisenbud
in the context of Green's conjecture on free resolutions of
canonical curves.
This is joint work with Stefan Papadima (arXiv:1011.5292, 1207.2038).
Mathematics Calendar 
Week of April 21, 2013
