Seminars and Colloquia by Series

Classification of Free Group Automorphisms

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

Loose Legendrians in high dimensional contact manifolds (II)

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

Loose Legendrians in high dimensional contact manifolds (I)

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

Braid and Knot Theory

Series
Geometry Topology Student Seminar
Time
Thursday, February 23, 2017 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sudipta Kolay – Georgia Tech
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.

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.

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