Seminars and Colloquia by Series

Wednesday, March 29, 2017 - 14:05 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Justin Lanier
Wednesday, March 22, 2017 - 14:05 , Location: Skiles 006 , None , None , Organizer: Justin Lanier
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.
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.

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