Geometry Seminar

Winter 2022

- Thursday February 17 at 3:30PM-4:30PM in Eckhart 202
- Maggie Miller, Stanford University
- Building concordances
- Abstract: I'll talk about one of my favorite theorems in 4-dimensional topology (or at least its implications), in which Hirose shows exactly which automorphisms of a genus-g surface can be achieved by smooth ambient isotopy in S^4 of an unknotted surface. This theorem is surprisingly useful, e.g. it can be used to reprove Kervaire's theorem that every smooth 2-sphere in S^4 bounds a smooth 3-ball into B^5 (my actual favorite theorem) with extra conditions on the embedding that Kervaire's argument does not achieve. I'll also show how to make use of these theorems to actually construct the knotted handlebodies that I'll describe on Wednesday in the colloquium..
- Thursday February 24 at 3:30PM-4:30PM in Eckhart 202
- Bena Tshishiku, Brown University
- Convex cocompact subgroups of the Goeritz group
- Abstract: This talk is about hyperbolicity of surface group extensions and a question of Farb-Mosher about whether purely pseudo-Anosov subgroups of mapping class groups are convex cocompact. I will explain this problem and give an answer for subgroups of the genus-2 Goeritz group, which is the group of mapping classes of a genus-2 surface that extend to the genus-2 Heegaard splitting of the 3-sphere.