Georgia Institute of Technology College of Sciences

The Weeks manifold W is a closed orientable hyperbolic 3-manifold with the smallest volume. Understanding contact structures on hyperbolic 3-manifolds is one of problems in contact topology. Stipsicz previously showed that there are 4 non-isotopic tight contact structures on the Weeks manifold. In this talk, we will exhibit 7 non-isotopic tight contact structures on W with non-vanishing Ozsvath-Szabo invariants.

In this series of talks we will show that every closed oriented three manifold is a branched cover over the three sphere, with some additional properties. In the first talk we will discuss some examples of branched coverings of surfaces and three manifolds, and a classical result of Alexander, which states that any closed oriented combinatorial manifold is always a branched cover over the sphere.

Much of what is known about automorphisms of free groups is given by analogy to results on mapping class groups. One desirable result is the celebrated Nielson-Thurston classification of the mapping class group into reducible, periodic, or pseudo Anosov homeomorphisms. We will discuss attempts at analogous results for free group automorphisms.