Seminars and Colloquia by Series

Colored Jones polynomials and Volume Conjecture, I

Series
Geometry Topology Student Seminar
Time
Wednesday, March 30, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Thao VuongGeorgia Tech
I will give an example of transforming a knot into closed braid form using Yamada-Vogel algorithm. From this we can write down the corresponding element of the knot in the braid group. Finally, the definition of a colored Jones polynomial is given using a Yang-Baxter operator. This is a preparation for next week's talk by Anh.

2-dimensional TQFTs and Frobenius Algebras

Series
Geometry Topology Student Seminar
Time
Wednesday, March 16, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alan DiazGeorgia Tech
( This will be a continuation of last week's talk. )An n-dimensional topological quantum field theory is a functor from the category of closed, oriented (n-1)-manifolds and n-dimensional cobordisms to the category of vector spaces and linear maps. Three and four dimensional TQFTs can be difficult to describe, but provide interesting invariants of n-manifolds and are the subjects of ongoing research. This talk focuses on the simpler case n=2, where TQFTs turn out to be equivalent, as categories, to Frobenius algebras. I'll introduce the two structures -- one topological, one algebraic -- explicitly describe the correspondence, and give some examples.

2-dimensional TQFTs and Frobenius Algebras

Series
Geometry Topology Student Seminar
Time
Wednesday, March 9, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alan DiazGeorgia Tech
An n-dimensional topological quantum field theory is a functor from the category of closed, oriented (n-1)-manifolds and n-dimensional cobordisms to the category of vector spaces and linear maps. Three and four dimensional TQFTs can be difficult to describe, but provide interesting invariants of n-manifolds and are the subjects of ongoing research. This talk focuses on the simpler case n=2, where TQFTs turn out to be equivalent, as categories, to Frobenius algebras. I'll introduce the two structures -- one topological, one algebraic -- explicitly describe the correspondence, and give some examples.

Souls of Some Convex Surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, March 2, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Eric ChoiEmory
The soul of a complete, noncompact, connected Riemannian manifold (M; g) of non-negative sectional curvature is a compact, totally convex, totally geodesic submanifold such that M is diffeomorphic to the normal bundle of the soul. Hence, understanding of the souls of M can reduce the study of M to the study of a compact set. Also, souls are metric invariants, so understanding how they behave under deformations of the metric is useful to analyzing the space of metrics on M. In particular, little is understood about the case when M = R2 . Convex surfaces of revolution in R3 are one class of two-dimensional Riemannian manifolds of nonnegative sectional curvature, and I will discuss some results regarding the sets of souls for some of such convex surfaces.

Exotic Four Manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, February 9, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bulent TosunGeorgia Tech
This will be a continuation of last week's talk on exotic four manifolds. We will recall the rational blow down operation and give a quick exotic example.

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