Seminars and Colloquia by Series

Taut foliations and Sutured Floer Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, November 15, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena HozooriGeorgia Tech
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.

A discussion of the the Lickorish Wallace Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, November 8, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva RoyGeorgia Tech
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'.

Lens space realization problem

Series
Geometry Topology Student Seminar
Time
Wednesday, October 18, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta KolayGeorgia Tech
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.

Computing Heegaard Floer homology by factoring mapping classes

Series
Geometry Topology Student Seminar
Time
Wednesday, October 11, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin LanierGeorgia Tech
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.

The Alexander polynomial

Series
Geometry Topology Student Seminar
Time
Wednesday, October 4, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Libby TaylorGeorgia Tech
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.

Null-Homotopic Embedded Spheres of Codimenion One

Series
Geometry Topology Student Seminar
Time
Wednesday, September 27, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav MukherjeeGeorgia Tech
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.

Braided embeddings of manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, September 20, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta KolayGeorgia Tech
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.

Tight contact structures on the Weeks manifold

Series
Geometry Topology Student Seminar
Time
Wednesday, September 13, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki MinGeorgia Tech
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.

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