Wednesday, October 19, 2016 - 14:00 , Location: Skiles 006 , Andrew McCullough , Georgia Institute of Technology , firstname.lastname@example.org , Organizer: Andrew McCullough
We will discuss some facts about intersection forms on closed, oriented 4-manifolds. We will also sketch the proof that for two closed, oriented, simply connected manifolds, they are homotopy equivalent if and only if they have isomorphic intersection forms.
Wednesday, October 5, 2016 - 14:00 , Location: Skiles 006 , Justin Lanier , Georgia Tech , Organizer: Justin Lanier
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.
Wednesday, September 28, 2016 - 14:05 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay
In this talk, we will discuss recent results by Ozawa on whether every compact submanifold of S^3 can be unknotted by twistings.
Wednesday, September 21, 2016 - 14:05 , Location: Skiles 006 , Balazs Strenner , Georgia Tech , Organizer: Balazs Strenner
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.
Wednesday, September 14, 2016 - 14:05 , Location: Skiles 006 , Shane Scott , Georgia Tech , email@example.com , Organizer: Shane Scott
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.
Tuesday, August 2, 2016 - 09:00 , Location: Skiles 006 , Andrew McCullough , Georgia Institute of Technology , firstname.lastname@example.org , Organizer: Andrew McCullough
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.