Seminars and Colloquia by Series

A Kirby calculus description of ribbon knots

Series
Geometry Topology Student Seminar
Time
Wednesday, February 22, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Andrew McCullough – Georgia Tech
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.

Conley-Zehnder index of periodic Reeb orbits

Series
Geometry Topology Student Seminar
Time
Wednesday, February 15, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena Hozoori – Georgia Tech
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.

Normal rulings of Legendrian links

Series
Geometry Topology Student Seminar
Time
Wednesday, February 8, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Caitlin Leverson – Georgia Tech
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.

Generating mapping class groups with two elements

Series
Geometry Topology Student Seminar
Time
Wednesday, February 1, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin Lanier – Georgia Tech
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.

Legendrian Contact Homology Examples

Series
Geometry Topology Student Seminar
Time
Wednesday, November 16, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Caitlin Leverson – Georgia Tech
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.

Legendrian Contact Homology Examples

Series
Geometry Topology Student Seminar
Time
Wednesday, November 9, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Caitlin Leverson – Georgia Tech
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.

Bounding 4-manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, November 2, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech
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.

Intersection forms and homotopy equivalence

Series
Geometry Topology Student Seminar
Time
Wednesday, October 19, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Andrew McCullough – Georgia Institute of Technology –
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.

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