Colloquium

Catherine Pfaff, Queen's University

"Deformation Spaces, R-Trees, & What Happens When You Iterate a Free Group Automorphism"

One of the most beautiful interplays in mathematics is between a deformation space and its symmetry group. Let X be a combinatorial object (such as a graph) or a topological object (such as a surface). Suppose X admits some further structure (such as a metric) in a nonunique way. Then the possible choices for the further structure are organized into a deformation space, on which a suitable group of symmetries of X acts. For a surface, this is the mapping class group acting on Teichmuller space, and for a graph, this is the free group outer automorphism group acting on Culler-Vogtmann Outer Space. We will discuss typical elements of these symmetry groups & the boundaries of the deformation spaces they act on, with special focus on the outer automorphism group of the free group and boundary of Culler-Vogtmann Outer Space. Results presented are joint work with I. Kapovich, J. Maher, and S.J. Taylor.

MC 5501