Skip to main content
Browse by:
GROUP

Until further notice, in-person public events have been canceled. Event listings include how to access online content.
Please check https://returnto.duke.edu/campus-visitors/ before coming to campus.

Mapping class groups and fiber bundles (Lecture 2)

Frontiers in Mathematics
Icon calendar
Friday, October 23, 2020
Icon time
12:00 pm - 1:00 pm
Icon speaker
Bena Tshishiku
Icon series
Frontiers in Mathematics Distinguished Lecture Series (Lecture 2)

We welcome the entire department to this Frontiers series!

The mapping class group Mod(M) of a smooth manifold M is the group of diffeomorphisms of M, modulo isotopy. Mapping class groups play an important role in geometric topology, especially in low dimensions, and they have connections to geometric group theory, dynamics, homotopy theory, algebraic geometry, and more. In these lectures we will give a broad overview of the theory of mapping class groups and then discuss two problems about these groups that relate to the study of fiber bundles. The first is the Nielsen realization problem, which asks when a subgroup of Mod(M) can be lifted to the diffeomorphism group Diff(M). The second is the "monodromy arithmeticity problem" of Griffiths-Schmid, which arises in the study of families of Riemann surfaces.

Contact: Lillian Pierce