Thursday, February 9
Time: 4:00 p.m.
Location: 114 McAllister Building
Name: William Goldman
Affiliation: University of Maryland
Title: Geometry and Dynamics of Surface Group Representations
Abstract: The space of representations of the fundamental group of a surface in a Lie group G is a rich geometric object. Examples include symplectic vector spaces, Jacobi varieties and Teichmueller spaces. The mapping class group acts on this space preserving a natural symplectic geometry. When is compact, the action is chaotic. For representations corresponding to geometric structures, the action has trivial dynamics (such as Teichmueller space).
For general G, the dynamics falls between these two extremes. For the simplest surfaces and G=SL(2), the dynamics reduces to an action (by polynomial diffeomorphisms) on the surfaces defined by the cubic polynomials
Curiously, nontrivial topology accompanies nontrivial dynamics, whereas trivial topology (Teichmueller space is contractible) accompanies trivial dynamics (the mapping class group acts properly).