Seminars and Colloquia by Series

Subgraphs of the curve graph

Series: Geometry Topology Student Seminar
Time: Wednesday, October 5, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location: Skiles 006
Speaker: Justin Lanier – Georgia Tech

Given a surface, intersection information about the simple closed curves on the surface is encoded in its curve graph. Vertices are homotopy classes of curves, and edges connect vertices corresponding to curves with disjoint representatives. We can wonder what subgraphs of the curve graph are possible for a given surface. For example, if we fix a surface, then a graph with sufficiently large clique number cannot be a subgraph of its curve graph. This is because there are only so many distinct and mutually disjoint curves in a given surface. We will discuss a new obstruction to a graph being a subgraph of individual curve graphs given recently by Bering, Conant, and Gaster.

Unknotting submanifolds of S^3 by twistings

Series: Geometry Topology Student Seminar
Time: Wednesday, September 28, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location: Skiles 006
Speaker: Sudipta Kolay – Georgia Tech

In this talk, we will discuss recent results by Ozawa on whether every compact submanifold of S^3 can be unknotted by twistings.

Penner's conjecture

Series: Geometry Topology Student Seminar
Time: Wednesday, September 21, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location: Skiles 006
Speaker: Balazs Strenner – Georgia Tech

In 1988, Penner conjectured that all pseudo-Anosov mapping classes arise up to finite power from a construction named after him. This conjecture was known to be true on some simple surfaces, including the torus, but has otherwise remained open. I will sketch the proof (joint work with Hyunshik Shin) that the conjecture is false for most surfaces.

Homological Stability of Automorphism Groups of Free Groups

Series: Geometry Topology Student Seminar
Time: Wednesday, September 14, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location: Skiles 006
Speaker: Shane Scott – Georgia Tech – scottsha@gatech.edu

Many algebraic results about free groups can be proven by considering a topological model suggested by Whitehead: glue two handlebodies trivially along their boundary to obtain a closed 3-manifold with free fundamental group. The complex of embedded spheres in the manifold gives a combinatorial model for the automorphism group of the free group. We will discuss how Hatcher uses this complex to show that the homology of the automorphism group is (eventually) independent of the rank of the free group.

Reducible surgeries and the cabling conjecture

Series: Geometry Topology Student Seminar
Time: Tuesday, August 2, 2016 - 09:00 for 1 hour (actually 50 minutes)
Location: Skiles 006
Speaker: Andrew McCullough – Georgia Institute of Technology – andrew.mccullough@gatech.edu

We will describe some recent work of Lidman, Sivek, and Yasui as it pertains to the cabling conjecture. This is a question about which Dehn surgeries in S^3 yeild reducible 3-manifolds.