Wednesday, January 24, 2018 - 13:55 , Location: Skiles 006 , Justin Lanier , GaTech , Organizer: Anubhav Mukherjee
Take a map from the interval [0,1] to itself. Such a map can be iterated, and many phenomena (such as periodic points) arise. An interval self-map is an example of a topological dynamical system that is simple enough to set up, but wildly complex to analyze. In the late 1970s, Milnor and Thurston developed a combinatorial framework for studying interval self-maps in their paper "Iterated maps of the interval". In this talk, we will give an introduction to the central questions in the study of iterated interval maps, share some illustrative examples, and lay out some of the techniques and results of Milnor and Thurston.
Wednesday, November 29, 2017 - 13:55 , Location: Skiles 006 , Anubhav Mukherjee , Georgia Tech , Organizer: Jennifer Hom
I'll try to describe some known facts about 3 manifolds. And in the end I want to give some idea about Geometrization Conjecture/theorem.
Wednesday, November 15, 2017 - 13:55 , Location: Skiles 006 , Surena Hozoori , Georgia Tech , Organizer: Jennifer Hom
It is known that a class of codimension one foliations, namely "taut foliations", have subtle relation with the topology of a 3-manifold. In early 80s, David Gabai introduced the theory of "sutured manifolds" to study these objects and more than 20 years later, Andres Juhasz developed a Floer type theory, namely "Sutured Floer Homology", that turned out to be very useful in answering the question of when a 3-manifold with boundary supports a taut foliation.
Wednesday, November 8, 2017 - 13:55 , Location: Skiles 006 , Agniva Roy , Georgia Tech , Organizer: Jennifer Hom
The Lickorish Wallace Theorem states that any closed 3-manifold is the result of a +/- 1-surgery on a link in S^3. I shall discuss the relevant definitions, and present the proof as outlined in Rolfsen's text 'Knots and Links' and Lickorish's 'Introduction to Knot Theory'.
Wednesday, October 18, 2017 - 13:55 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Jennifer Hom
I will talk about the Berge conjecture, and Josh Greene's resolution of a related problem, about which lens spaces can be obtained by integer surgery on a knot in S^3.
Wednesday, October 11, 2017 - 13:55 , Location: Skiles 006 , Justin Lanier , Georgia Tech , Organizer: Jennifer Hom
We will discuss the mapping class groupoid, how it is generated by handle slides, and how factoring in the mapping class groupoid can be used to compute Heegaard Floer homology. This talk is based on work by Lipshitz, Ozsvath, and Thurston.
Wednesday, October 4, 2017 - 13:55 , Location: Skiles 006 , Libby Taylor , Georgia Tech , Organizer: Jennifer Hom
Let K be a tame knot in S^3. Then the Alexander polynomial is knot invariant, which consists of a Laurent polynomial arising from the infinite cyclic cover of the knot complement. We will discuss the construction of the Alexander polynomial and, more generally, the Alexander invariant from a Seifert form on the knot. In addition, we will see some connections between the Alexander polynomial and other knot invariants, such as the genus and crossing number.
Wednesday, September 27, 2017 - 13:55 , Location: Skiles 006 , Anubhav Mukherjee , Georgia Tech , Organizer: Justin Lanier
Let S be an (n-1)-sphere smoothly embedded in a closed, orientable, smooth n-manifold M, and let the embedding be null-homotopic. We'll prove in the talk that, if S does not bound a ball, then M is a rational homology sphere, the fundamental group of both components of M\S are finite, and at least one of them is trivial. This talk is based on a paper of Daniel Ruberman.
Wednesday, September 20, 2017 - 13:55 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay
The theory of braids has been very useful in the study of (classical) knot theory. One can hope that higher dimensional braids will play a similar role in higher dimensional knot theory. In this talk we will introduce the concept of braided embeddings of manifolds, and discuss some natural questions about them.
Wednesday, September 13, 2017 - 13:55 , Location: Skiles 006 , Hyun Ki Min , Georgia Tech , Organizer: Jennifer Hom
The Weeks manifold W is a closed orientable hyperbolic 3-manifold with the smallest volume. Understanding contact structures on hyperbolic 3-manifolds is one of problems in contact topology. Stipsicz previously showed that there are 4 non-isotopic tight contact structures on the Weeks manifold. In this talk, we will exhibit 7 non-isotopic tight contact structures on W with non-vanishing Ozsvath-Szabo invariants.