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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.

Wednesday, February 8, 2017 - 14:05 ,
Location: Skiles 006 ,
Caitlin Leverson ,
Georgia Tech ,
Organizer: Justin Lanier

Normal rulings are decompositions of a projection of a Legendrian knot
or link. Not every link has a normal ruling, so existence of a normal
ruling gives a Legendrian link invariant. However, one can use the
normal rulings of a link to define the ruling
polynomial of a link, which is a more useful Legendrian knot invariant.
In this talk, we will discuss normal rulings of Legendrian links in
various manifolds and prove that the ruling polynomial is a Legendrian
link invariant.

Wednesday, February 1, 2017 - 14:05 ,
Location: Skiles 006 ,
Justin Lanier ,
Georgia Tech ,
Organizer: Justin Lanier

Wajnryb showed that the mapping class group of a surface can be generated by two elements, each given as a product of Dehn twists. We will discuss a follow-up paper by Korkmaz, "Generating the surface mapping class group by two elements." Korkmaz shows that one of the generators may be taken to be a single Dehn twist instead. He then uses his construction to further prove the striking fact that the two generators can be taken to be periodic elements, each of order 4g+2, where g is the genus of the surface.

Wednesday, November 16, 2016 - 14:05 ,
Location: Skiles 006 ,
Caitlin Leverson ,
Georgia Tech ,
Organizer: Shane Scott

We will review the definition of the Chekanov-Eliashberg differentialgraded algebra for Legendrian knots in R^3 and look at examples tounderstand a few of the invariants that come from Legendrian contacthomology.

Wednesday, November 9, 2016 - 14:05 ,
Location: Skiles 006 ,
Caitlin Leverson ,
Georgia Tech ,
Organizer: Shane Scott
We will review the definition of the Chekanov-Eliashberg differentialgraded algebra for Legendrian knots in R^3 and look at examples tounderstand a few of the invariants that come from Legendrian contacthomology.

Wednesday, November 2, 2016 - 14:05 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Sudipta Kolay

We will show that every closed orientable 3-manifold bounds an orientable 4-manifold. If time permits, we will also see an application to embedding closed orientable 3-manifolds to R^5.