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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.

Wednesday, October 19, 2016 - 14:00 ,
Location: Skiles 006 ,
Andrew McCullough ,
Georgia Institute of Technology ,
andrew.mccullough@gatech.edu ,
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.