Geometry, Topology and Dynamics Seminar
Nick Salter
University of Chicago
Mapping class groups and monodromy of some families of algebraic curves
Abstract: Complex algebraic geometry is a wonderfully rich source of
geometric/topological phenomena. In this talk, I will survey some
connections between classical notions in algebraic geometry (e.g. smooth
algebraic curves in the projective plane) and low-dimensional topology,
particularly the mapping class group. The connection arises through the
notion of a “Riemann surface bundle”. A “family” of algebraic curves
arising via algebraic geometry naturally forms such a fiber bundle, and
any such bundle has a monodromy representation, i.e. a subgroup of the
mapping class group. These groups are rich and interesting, but currently
very poorly understood. I will discuss some work of mine in this direction
- one result constrains the size of these groups, and another shows they
are quite large in certain contexts. This will involve a blend of ideas
from algebraic geometry and the theory of the mapping class group,
particularly the Torelli group.
Monday April 3, 2017 at 3:00 PM in SEO 636