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Wednesday, September 27, 2017 - 13:55 ,
Location: Skiles 006 ,
Anubhav Mukherjee ,
Georgia Tech ,
Organizer: Justin Lanier

Let S be an (n-1)-sphere smoothly embedded in a closed, orientable, smooth n-manifold M, and let the embedding be null-homotopic. We'll prove in the talk that, if S does not bound a ball, then M is a rational homology sphere, the fundamental group of both components of M\S are finite, and at least one of them is trivial. This talk is based on a paper of Daniel Ruberman.

Wednesday, September 20, 2017 - 13:55 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Sudipta Kolay

The theory of braids has been very useful in the study of (classical)
knot theory. One can hope that higher dimensional braids will play a
similar role in higher dimensional knot theory. In this talk we will introduce the concept of braided embeddings of manifolds, and discuss some natural questions about them.

Wednesday, September 13, 2017 - 13:55 ,
Location: Skiles 006 ,
Hyun Ki Min ,
Georgia Tech ,
Organizer: Jennifer Hom

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.

Wednesday, April 5, 2017 - 14:05 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Justin Lanier

Continuing from last time, we will discuss Hilden and Montesinos' result
that every smooth closed oriented three manifold is a three fold
branched cover over the three sphere, and also there is a representation
by bands.

Wednesday, March 29, 2017 - 14:05 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Justin Lanier

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.

Wednesday, March 15, 2017 - 14:05 ,
Location: Skiles 006 ,
Shane Scott ,
Georgia Tech ,
Organizer: Justin Lanier

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.

Wednesday, March 8, 2017 - 14:05 ,
Location: Skiles 006 ,
Hyun Ki Min ,
Georgia Tech ,
Organizer: Justin Lanier

There
is no general h-principle for Legendrian embeddings in contact
manifolds. In dimension 3, however, Legendrian knots in the complement
of an overtwisted disc, which are called
loose, satisfy an h-principle. We will discuss the high dimensional
analog of loose knots.