- Series
- Dissertation Defense
- Time
- Friday, April 5, 2024 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 169
- Speaker
- Roberta Shapiro – Georgia Tech
- Organizer
- Roberta Shapiro
The goal of this talk is to explore curve graphs, which are combinatorial tools that encode topological information about surfaces. We focus on variants of the fine curve graph of a surface. The fine curve graph has its vertices essential simple closed curves on the surface and its edges connect pairs of curves that are disjoint. We will mention a sampling of related theorems which were proven in collaboration with various coauthors and then prove several results regarding the finitary curve graph, which has as its vertices essential simple closed curves while its edges connect pairs of curves that intersect at finitely many points.
In this talk, we will prove that the finitary curve graph has diameter 2 (geometry), that the flag complex induced by the finitary curve graph is contractible (topology), and that the automorphism group of the finitary curve graph is naturally isomorphic to the homeomorphism group of the surface (combinatorics).
Work mentioned in the talk will be a subset of independent work and of collaborations with Katherine Booth, Ryan Dickmann, Dan Minahan, and Alex Nolte. The talk will be aimed at a non-expert audience.