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Friday, November 12, 2010 - 14:00 ,
Location: Skiles 171 ,
Jean Bellissard ,
Ga Tech ,
Organizer: John Etnyre

Note this is a 2 hour talk.

In this lecture, we will look at the notion of crossed product by a group action. The example of the non commutative torus will be considered in detail. The analog of vector fields, vector bundle and connection will be introduced from this example. Some example of connection will be described and the curvature will be computed.

Friday, October 29, 2010 - 14:00 ,
Location: Skiles 171 ,
Jean Bellissard ,
Ga Tech ,
Organizer: John Etnyre

Note this is a 2 hour talk.

An action of the real line on a compact manifold defines a topological dynamical system. The set of orbits might be very singular for the quotient topology. It will be shown that there is, however, a C*-algebra, called the crossed product, which encodes the topology of the orbit space. The construction of this algebra can be done for an group action, if the group is locally compact.

Friday, October 15, 2010 - 14:00 ,
Location: Skiles 171 ,
Jean Bellissard ,
Ga Tech ,
Organizer: John Etnyre

Note this is a 2 hour talk.

This series of lecture will try to give some basic facts about Noncommutative Geometry for the members of the School of Mathematics who want to learn about it. In the first lecture, the basics tools will be presented, (i) the philosophy and the notion of space, and (ii) the notion of C*-algebra, (iii) groupoids. As many examples as possible will be described to illustrate the purpose. In the following lectures, in addition to describing these tools more thoroughly, two aspects can be developed depending upon the wishes of the audience: A- Topology, K-theory, cyclic cohomology B- Noncommutative metric spaces and Riemannian Geometry.

Friday, October 8, 2010 - 14:00 ,
Location: Skiles 171 ,
Jean Bellissard ,
Ga Tech ,
Organizer: John Etnyre
This series of lecture will try to give some basic facts about Noncommutative Geometry for the members of the School of Mathematics who want to learn about it. In the first lecture, the basics tools will be presented, (i) the philosophy and the notion of space, and (ii) the notion of C*-algebra, (iii) groupoids. As many examples as possible will be described to illustrate the purpose. In the following lectures, in addition to describing these tools more thoroughly, two aspects can be developed depending upon the wishes of the audience: A- Topology, K-theory, cyclic cohomology B- Noncommutative metric spaces and Riemannian Geometry.

Note this is a 2 hour talk (with a short break in the middle).

Friday, October 1, 2010 - 14:00 ,
Location: Skiles 171 ,
John Etnyre and/or Amey Kaloti ,
Ga Tech ,
Organizer: John Etnyre

In this talk we will give an introduction of Heegaard-Floer theory through examples. By exploring several explicit examples we hope to show that various aspects of the definitions that seem complicated, really aren't too bad and it really is possible to work with these fairly abstract things. While this is technically a continuation of last weeks talk, we will review enough material so that this talk should be self contained.

Friday, September 24, 2010 - 14:00 ,
Location: Skiles 171 ,
Amey Kaloti ,
Ga Tech ,
Organizer: John Etnyre

This will be an introduction to the basic aspects of Heegaard-Floer homology and knot Heegaard-Floer homology. After this talk (talks) we will be organizing a working group to go through various computations and results in knot Heegaard-Floer theory and invariants of Legendrian knots.

Friday, September 17, 2010 - 14:00 ,
Location: Skiles 171 ,
Dan Margalit ,
Georgia Tech ,
Organizer: Dan Margalit

We will prove that the mapping class group is finitely presented, using its action on the arc complex. We will also use the curve complex to show that the abstract commensurator of the mapping class group is the extended mapping class group. If time allows, we will introduce the complex of minimizing cycles for a surface, and use it to compute the cohomological dimension of the Torelli subgroup of the mapping class group. This is a followup to the previous talk, but will be logically independent.

Thursday, September 9, 2010 - 11:00 ,
Location: Skiles 269 ,
Amey Kaloti ,
Georgia Tech. ,
ameyk@math.gatech.edu ,
Organizer:

This talk is part of the oral exam for the speaker. Please note the special time, place. Also the talk itself will be 45 min long.

Non-loose knots is a special class of knots studied in contact geometry. Last couple of years have shown some applications of these kinds of knots. Even though defined for a long time, not much is known about their classification except for the case of unknot. In this talk we will summarize what is known and tell about the recent work in which we are trying to give classification in the case of trefoil.