Seminars and Colloquia by Series

Friday, October 8, 2010 - 14:00 , Location: Skiles 171 , Jean Bellissard , Ga Tech , Organizer: John Etnyre

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

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 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.
Friday, September 3, 2010 - 13:00 , Location: Skiles 114 , Dan Margalit , Georgia Tech , Organizer: Dan Margalit
The mapping class group is the group of symmetries of a surface (modulo homotopy).  One way to study the mapping class group of a surface S is to understand its action on the set of simple closed curves in S (up to homotopy).  The set of homotopy classes of simple closed curves can be organized into a simplicial complex called the complex of curves.  This complex has some amazing features, and we will use it to prove a variety of theorems about the mapping class group.  We will also state some open questions.  This talk will be accessible to second year graduate students.
Friday, April 23, 2010 - 14:00 , Location: Skiles 269 , Thao Vuong , Georgia Tech , Organizer:
We will give definitions and then review a result by Floyd and Oertel that in a Haken 3-manifold M, there are a finite number of branched surfaces whose fibered neighborhoods contain all the incompressible, boundary-incompressible surfaces in M, up to isotopy. A corollary of this is that the set of boundary slopes of a knot K in S^3 is finite.
Friday, April 16, 2010 - 14:00 , Location: Skiles 269 , Igor Belegradek , Georgia Tech , Organizer:
I will discuss moduli spaces of Riemannian metrics with various curvature conditions, and then focus on the case of nonnegative sectional curvature.
Friday, April 9, 2010 - 14:00 , Location: Skiles 269 , Igor Belegradek , School of Mathematics, Georgia Tech , Organizer:
I will review results on the structure of open nonnegatively curved manifolds due to Cheeger-Gromoll, Perelman, and Wilking.
Friday, March 19, 2010 - 14:00 , Location: Skiles 269 , Alan Diaz , School of Mathematics, Georgia Tech , Organizer:
Last week we motivated and defined Khovanov homology, an invariant of oriented links whose graded Euler characteristic is the Jones polynomial. We'll discuss the proof of Reidemeister invariance, then survey some important applications and extensions, including Lee theory and Rasmussen's s-invariant, the connection to knot Floer homology, and how the latter was used by Hedden and Watson to show unknot detection for a large class of knots.

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