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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.

Wednesday, March 1, 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.

Thursday, February 23, 2017 - 12:00 ,
Location: Skiles 005 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Sudipta Kolay

Braid and knot theory in 3-dimensional Euclidean space are related by classical theorems of Alexander and Markov. We will talk about closed braids in higher dimensions, and generalizations of Alexander's theorem.

Wednesday, February 22, 2017 - 14:05 ,
Location: Skiles 006 ,
Andrew McCullough ,
Georgia Tech ,
Organizer: Justin Lanier

We will discuss a way of explicitly constructing ribbon knots using
one-two handle canceling pairs. We will also mention how this is
related to some recent work of Yasui, namely that there are infinitely
many knots in
(S^3, std) with negative maximal Thurston-Bennequin invariant for which
Legendrian surgery yields a reducible manifold.

Wednesday, February 15, 2017 - 14:05 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Tech ,
Organizer: Justin Lanier

In this talk, I will define Conley-Zehnder index of a periodic Reeb
orbit and will give several characterizations of this invariant.
Conley-Zehnder index plays an important role in computing the dimension
of certain families of J-holomorphic curves in the symplectization of a
contact manifold.