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Wednesday, August 29, 2012 - 14:00 ,
Location: Skiles 006 ,
Hyunshik Shin ,
School of Mathematics, Georgia Tech ,
Organizer:

We will discuss the basics of automorphisms of free groups and train track
structure. We will define the growth rate which is a topological entropy
of the train track map.

Wednesday, February 8, 2012 - 14:05 ,
Location: Skiles 169 ,
Jonathan Paprocki ,
Georgia Tech ,
Organizer:

We will prove a duality between locally compact Hausdorff spaces and the C*-algebra of continuous complex-valued functions on that space. Formally, this is the equivalence of the opposite category of commutative C*-algebras and the category of locally compact Hausdorff spaces.

Wednesday, January 25, 2012 - 14:00 ,
Location: Skiles 005 ,
Bulent Tosun ,
Georgia Tech ,
Organizer:

The aim of the talk is to give a complete proof of the fact that any closed oriented 3-manifold has a trivial tangent bundle.

Wednesday, November 9, 2011 - 14:05 ,
Location: Skiles 005 ,
Alan Diaz ,
Georgia Tech ,
Organizer:

TBA

Wednesday, November 2, 2011 - 14:05 ,
Location: Skiles 005 ,
Eric Choi ,
Emory University ,
Organizer:

Knowledge of rays and critical points of infinity in von Mangoldt planes can be applied to understanding the structure of open complete manifolds with lower radial curvature bounds. We will show how the set of souls is computed for every von Mangoldt plane of nonnegative curvature. We will also make some observations on the structure of the set of critical points of infinity for von Mangoldt planes with negative curvature.

Wednesday, October 26, 2011 - 14:00 ,
Location: Skiles 005 ,
Meredith Casey ,
Georgia Tech ,
Organizer:

The main purpose of this talk is to better understand how to use branched covers to construct 3-manifolds. We will start with branched covers of 2-manifolds, carefully working through examples and learning the technology. Using these methods in combination with open book decompositions we will show how to construct 3-manifolds by branching over link and knots in S^{3}. Particular emphasis will be placed on using the map to get a "coloring" of the branched locus and how this combinatorial data is useful both for explicit constructions and for the general theory.

Wednesday, October 19, 2011 - 14:05 ,
Location: Skiles 005 ,
Amey Kaloti ,
Georgia Tech ,
Organizer:

In this talk we will outline proof due to Plameneveskaya and Van-Horn
Morris that every virtually overtwisted contact structure on L(p,1) has a
unique Stein filling. We will give a much simplified proof of this
result. In addition, we will talk about classifying Stein fillings of
($L(p,q), \xi_{std})$ using only mapping class group basics.

Wednesday, October 5, 2011 - 14:05 ,
Location: Skiles 005 ,
Amey Kaloti ,
Georgia Tech ,
Organizer:
In this talk we will outline proof due to Plameneveskaya and Van-Horn
Morris that every virtually overtwisted contact structure on L(p,1) has a
unique Stein filling. We will give a much simplified proof of this
result. In addition, we will talk about classifying Stein fillings of
($L(p,q), \xi_{std})$ using only mapping class group basics.

Wednesday, September 28, 2011 - 14:05 ,
Location: Skiles 005 ,
Marta Aguilera ,
Georgia Tech ,
Organizer:

In this talk I define the braid groups, its Garside structure, and its
application to solve the word and conjugacy problems. I present a braid
group with $n$ strands as the mapping class group of the disk with $n$
punctures, $\mathbb{D}^2-\{p_1\ldots p_n\}$, and a classification of
surface homeomorphisms by the Nielsen Thurston theorem. I will also
discuss results that require algebraic and geometric tools.

Wednesday, September 7, 2011 - 14:05 ,
Location: Skiles 005 ,
Bulent Tosun ,
Georgia Tech ,
Organizer:

Continuation of last week's talk