Seminars and Colloquia by Series

A Riemannian geometry look at contact geometry

Series
Geometry Topology Working Seminar
Time
Friday, February 11, 2011 - 14:00 for 2 hours
Location
Skiles 269
Speaker
John Etnyre – School of Mathematics, Georgia Tech
This is part two of a lecture series investigating questions in contact geometry from the perspective of Riemannian geometry. Interesting questions in Riemannian geometry arising from contact geometry have a long and rich history, but there have been few applications of Riemannian geometry to contact topology. In these talks I will discuss basic connections between Riemannian and contact geometry and some applications of these connections. I will also discuss the "contact sphere theorem" that Rafal Komendarczyk, Patrick Massot and I recently proved as well as other results.

A Riemannian geometry look at contact geometry

Series
Geometry Topology Working Seminar
Time
Friday, February 4, 2011 - 14:00 for 2 hours
Location
Skiles 269
Speaker
John Etnyre – Ga Tech
This will be the first of a two part lecture series investigating questions in contact geometry from the perspective of Riemannian geometry. Interesting questions in Riemannian geometry arising from contact geometry have a long and rich history, but there have been few applications of Riemannian geometry to contact topology. In these talks I will discuss basic connections between Riemannian and contact geometry and some applications of these connections. I will also discuss the "contact sphere theorem" that Rafal Komendarczyk, Patrick Massot and I recently proved as well as other results.

Non-commutative Geometry VI - Riemannian Geometry of Ultrametric Cantor Sets

Series
Geometry Topology Working Seminar
Time
Friday, December 10, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Jean Bellissard – Ga Tech

Please Note: Note this is a two hour seminar.

In this lecture the analog of Riemannian manifold will be introduced through the notion of spectral triple. The recent work on the case of a metric Cantor set, endowed with an ultrametric, will be described in detail during this lecture. An analog of the Laplace Beltrami operator for a metric Cantor set will be defined and studied.

Non-commutative Geometry V - Riemannian Geometry of Ultrametric Cantor Sets

Series
Geometry Topology Working Seminar
Time
Friday, December 3, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Jean Bellissard – Ga Tech

Please Note: This will be a 2 hour talk.

In this lecture the analog of Riemannian manifold will be introduced through the notion of spectral triple. The recent work on the case of a metric Cantor set, endowed with an ultrametric, will be described in detail during this lecture. An analog of the Laplace Beltrami operator for a metric Cantor set will be defined and studied

Non-commutative Geometry IV - Crossed products: the noncommutative torus

Series
Geometry Topology Working Seminar
Time
Friday, November 12, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Jean Bellissard – Ga Tech

Please Note: 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.

Non-commutative Geometry III: Crossed Product and Orbit Space of Group Actions

Series
Geometry Topology Working Seminar
Time
Friday, October 29, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Jean Bellissard – Ga Tech

Please Note: 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.

Non-commutative Geometry II

Series
Geometry Topology Working Seminar
Time
Friday, October 15, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Jean Bellissard – Ga Tech

Please Note: 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.

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