Student GFA Seminar Schedule 2005-2006
| September 20th | Uuye Otgonbayar |
Commutative C^*-algebras I will talk about commutative C^*-algebras and von Neumann algebras, including the Gelfand-Naimark theorem John mentioned last Monday. This should give some justification of why GFA is referred to as noncommutative geometry sometimes. |
| September 27th | Bram Mesland |
K-theory and Serre-Swan's Theorem |
| October 4th | Robert Yuncken |
Introduction to C^*-algebras, Part I I'm going to start off just talking about non-commutative geometry in general - ie, what is it and what's it good for? So there'll be some (very) basic examples to start with. But as an application, I'll go to group C^*-algebras. Hopefully I'll have a chance to prove Powers Theorem by the end of the hour. That theorem says, roughly, that the space of representations of the free group is a _connected_ noncommutative space. |
| October 11th | Robert Yuncken |
Introduction to C^*-algebras, Part II |
| October 18th | Tyrone Crisp |
Crossed product algebras I'm thinking of talking about C^*-algebra crossed products (at a very elementary level) - it seems to me that this would tie in nicely with what we've already done, i.e. continuing the idea of taking concepts from other areas of mathematics (symmetry, dynamical systems) and translating them into the realm of C^*-algebras. Also this would pave the way for me to talk some time in the future about graph algebras and in particular the very nice and very easy computation of their K-theory, which relies on the dual Pimsner-Voiculescu exact sequence for crossed products by the circle group. |
| October 25th | Uuye Otgonbayar |
Morita Equivalence for C^*-algebras |
| November 1th | Bram Mesland |
Exact sequences in algebraic K_0 and K_1 |
| November 8th | Daniele Signori |
Quantization, Moyal Product and Asymptotic Morphisms, Part I The Unofficial Physics-Maths Dictionary reports Quantum = Noncommutative. "Quantization" is thus a machinery producing noncummmutativity out of commutativity. There's an endless number of such devices. The Moyal product - a special case of Deformation Quantization - will be today's inspirational topic for the introduction of some algebra (a version of the Hochschild Complex) and some analysis (Asymptotic morphisms of C^*-algebras). |
| November 15th | Daniele Signori |
Quantization, Moyal Product and Asymptotic Morphisms, Part II |
| November 29th | Uuye Otgonbayar | Bott Periodicity in K-Theory, Part I
I will talk about homotopy theoretic aspects of K-theory for topological spaces and higher K-theory. Then I'll prove the Bott Periodicity theorem using the Moyal quantizer. |
| December 6th | Uuye Otgonbayar | Bott Periodicity in K-Theory, Part II
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