Topology Advanced Classes
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Mon, 16/01/2012 11:00 |
Gua Thiang, Robert Laugwitz, Jan Vonk |
Topology Advanced Classes  |
L3 |
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Three short talks by the authors of essays on topics related to c3 Algebraic topology: Whitehead's theorem, Cohomology of fibre bundles, Division algebras |
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Mon, 30/01/2012 11:00 |
Andre Henriques (Utrecht) |
Topology Advanced Classes |
L3 |
| The idea of three-tier conformal field theory (CFT) was first proposed by Greame Segal. It is an extension of the functorial approach to CFT, where one replaces the bordism category of Riemann surfaces by a suitable bordism 2-category, whose objects are points, whose morphism are 1-manifolds, and whose 2-morphisms are pieces of Riemann surface. The Baez-Dolan cobordism hypothesis is a meta-mathematical principle. It claims that functorial quantum field theory (i.e. quantum field theory expressed as a functor from some bordism category) becomes simper once "you go all the way down to points", i.e., once you replace the bordism category by a higher category. Three-tier CFT is an example of "going all the way down to points". We will apply the cobordism hypothesis to the case of three-tier CFT, and show how the modular invariance of the partition function can be derived as a consequence of the formalism, even if one only starts with genus-zero data. | |||
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Mon, 06/02/2012 11:00 |
Leo Corry (Tel Aviv) |
Topology Advanced Classes |
L3 |
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Mon, 05/03/2012 11:00 |
James Griffin (Cambridge) |
Topology Advanced Classes |
L3 |
| A cactus product is much like a wedge product of pointed spaces, but instead of being uniquely defined there is a moduli space of possible cactus products. I will discuss how this space can be interpreted geometrically and how its combinatorics calculates the homology of the automorphism group of a free product with no free group factors. Then I will reinterpret the moduli space with Outer space in mind: the lobes of the cacti now behave like boundaries and our free products can now include free group factors. | |||
