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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.

Wednesday, February 23, 2011 - 11:00 ,
Location: Skiles 006 ,
Becca Winarski ,
Georgia Tech ,
Organizer:

Wednesday, February 16, 2011 - 11:00 ,
Location: Skiles 006 ,
Meredith Casey ,
Georgia Tech ,
Organizer:

TBA

Wednesday, February 9, 2011 - 11:00 ,
Location: Skiles 006 ,
Bulent Tosun ,
Georgia Tech ,
Organizer:

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.

Wednesday, February 2, 2011 - 11:00 ,
Location: Skiles 006 ,
Bulent Tosun ,
Georgia Tech ,
Organizer:

I will talk about rational blow down operation and give a quick exotic example.