Thursday, November 29, 2007, 3:30 p.m.

South Hall Room 6635

(Refreshments at 3:00 p.m.)

Abstract: An ``outer space" for a group G is a contractible space with a proper action of the group Out(G) of outer automorphisms of G. Classical examples include homogeneous spaces and Teichmuller spaces. For a free group F of finite rank, an outer space was introduced in the mid-1980's. The basic idea is to think of an automorphism of a free group topologically, as a homotopy equivalence of a finite graph. In this talk I will describe Outer space and explain how it is used to obtain algebraic information about Out(F_n), and then indicate how ideas from Outer space are currently expanding in new directions.

Friday, November 30, 2007, 3:30 p.m.

South Hall Room 6635

Abstract: This is joint work with Ruth Charney. Right-angled Artin groups (RAAG's) interpolate between free groups and free abelian groups: they are described by giving a set of generators, some of which commute. RAAG's are conveniently described by drawing a graph whose vertices are the generators of the RAAG, with an edge between two generators if and only if they commute. We discuss progress on understanding finiteness properties of the group of outer automorphisms of a RAAG, particularly in the case when the associated graph is a tree. The graph is a tree if and only if the associated RAAG is a 3-manifold group.