Seminars and Colloquia by Series

Multisections, the pants complex, and Weinstein manifolds

Series
Geometry Topology Seminar
Time
Monday, December 5, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gabriel IslambouliUC Davis

We introduce a decomposition of a 4-manifold called a multisection, which is a mild generalization of a trisection. We show that these correspond to loops in the pants complex and provide an equivalence between closed smooth 4-manifolds and loops in the pants complex up to certain moves. In another direction, we will consider multisections with boundary and show that these can be made compatible with a Weinstein structure, so that any Weinstein 4-manifold can be presented as a collection of curves on a surface.

Geography of surface bundles over surfaces

Series
Geometry Topology Seminar
Time
Monday, October 3, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
İnanç BaykurUMass Amherst / Harvard

An outstanding problem for surface bundles over surfaces, closely related to the symplectic geography problem in dimension four, is to determine for which fiber and base genera there are examples with non-zero signatures. I will report on our recent progress (joint with M. Korkmaz), which resolves the problem for all fiber and base genera except for 18 pairs at the time of writing.

The stable cohomology of the level-l subgroup of the mapping class group (Joint Topology Seminar @ UGA)

Series
Geometry Topology Seminar
Time
Monday, September 26, 2022 - 16:30 for 1 hour (actually 50 minutes)
Location
University of Georgia (Boyd 322)
Speaker
Andrew PutmanNotre Dame

After an introduction to how to think about the mapping class groupand its cohomology, I will discuss a recent theorem of mine saying
that passing to the level-l subgroup does not change the rational cohomology in a stable range.

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