Representation Theory Seminar
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Thu, 11/10/2007 14:30 |
Jan Grabowski (Oxford) |
Representation Theory Seminar  |
L3 |
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Thu, 18/10/2007 14:30 |
Jeremie Guilhot (Aberdeen) |
Representation Theory Seminar |
L3 |
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Thu, 25/10/2007 14:30 |
Mark Wildon (Swansea/Oxford) |
Representation Theory Seminar |
L3 |
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Thu, 01/11/2007 13:30 |
Bernhard Keller (Paris) |
Representation Theory Seminar |
L3 |
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Thu, 08/11/2007 13:30 |
Steffen Oppermann (Trondheim) |
Representation Theory Seminar |
L3 |
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Thu, 15/11/2007 13:30 |
Matthew Grime (Bristol) |
Representation Theory Seminar |
L3 |
| There are many triangulated categories that arise in the study of group cohomology: the derived, stable or homotopy categories, for example. In this talk I shall describe the relative cohomological versions and the relationship with ordinary cohomology. I will explain what we know (and what we would like to know) about these categories, and how the representation type of certain subgroups makes a fundamental difference. | |||
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Thu, 22/11/2007 13:30 |
Catharina Stroppel (Glasgow) |
Representation Theory Seminar |
L3 |
| I will discuss how one can construct nice cellular algebras using the cohomology of Springer fibres associated with two block nilpotent matrices (and the convolution product). Their quasi-hereditary covers can be described via categories of highest weight modules for the Lie algebra sl(n). The combinatorics of torus fixed points in the Springer fibre describes decomposition multiplicities for the corresponding highest weight categories. As a result one gets a natural subcategory of coherent sheaves on a resolution of the slice to the corresponding nilpotent orbit. | |||
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Thu, 29/11/2007 13:30 |
Eugenia Cheng (Sheffield) |
Representation Theory Seminar |
L3 |
| Category theory is used to study structures in various branches of mathematics, and higher-dimensional category theory is being developed to study higher-dimensional versions of those structures. Examples include higher homotopy theory, higher stacks and gerbes, extended TQFTs, concurrency, type theory, and higher-dimensional representation theory. In this talk we will present two general methods for "categorifying" things, that is, for adding extra dimensions: enrichment and internalisation. We will show how these have been applied to the definition and study of 2-vector spaces, with 2-representation theory in mind. This talk will be introductory; in particular it should not be necessary to be familiar with any category theory other than the basic idea of categories and functors. | |||
