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Wednesday, July 6, 2011 - 14:00 ,
Location: Skiles 005 ,
Anh Tran ,
Georgia Tech ,
Organizer:

I will define character varieties of finitely generated groups and consider some applications of them in geometry/topology.

Wednesday, June 1, 2011 - 14:00 ,
Location: Skiles 005 ,
Becca Winarski ,
Georgia Tech ,
Organizer:

Wednesday, May 25, 2011 - 14:00 ,
Location: Skiles 006 ,
Meredith Casey ,
Georgia Tech ,
Organizer:

Wednesday, April 20, 2011 - 11:00 ,
Location: Skiles 006 ,
Bulent Tosun ,
Georgia Tech ,
Organizer:

Wednesday, April 13, 2011 - 11:00 ,
Location: Skiles 006 ,
Amey Kaloti ,
Georgia Tech ,
Organizer:

Wednesday, April 6, 2011 - 11:00 ,
Location: Skiles 006 ,
Anh Tran ,
Georgia Tech ,
Organizer:

TBA

Wednesday, March 30, 2011 - 11:00 ,
Location: Skiles 006 ,
Thao Vuong ,
Georgia Tech ,
Organizer:

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.

Wednesday, March 16, 2011 - 11:00 ,
Location: Skiles 006 ,
Alan Diaz ,
Georgia Tech ,
Organizer:

( 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.

Wednesday, March 9, 2011 - 11:00 ,
Location: Skiles 006 ,
Alan Diaz ,
Georgia Tech ,
Organizer:

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.

Wednesday, March 2, 2011 - 11:00 ,
Location: Skiles 006 ,
Eric Choi ,
Emory ,
Organizer:

The soul of a complete, noncompact, connected Riemannian manifold (M; g)
of nonnegative sectional curvature is a compact, totally convex, totally geodesic
submanifold such that M is dieomorphic 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.