Algebra Seminar
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Tue, 28/04/2009 17:00 |
Peter Fiebig (Universitat Freiburg) |
Algebra Seminar  |
L2 |
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Tue, 05/05/2009 17:00 |
Christopher Voll (Southampton) |
Algebra Seminar |
L2 |
| The study of representation growth of infinite groups asks how the numbers of (suitable equivalence classes of) irreducible n-dimensional representations of a given group behave as n tends to infinity. Recent works in this young subject area have exhibited interesting arithmetic and analytical properties of these sequences, often in the context of semi-simple arithmetic groups. In my talk I will present results on the representation growth of some classes of finitely generated nilpotent groups. They draw on methods from the theory of zeta functions of groups, the (Kirillov-Howe) coadjoint orbit formalism for nilpotent groups, and the combinatorics of (finite) Coxeter groups. | |||
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Tue, 12/05/2009 17:00 |
Erika Damian (University of East Anglia) |
Algebra Seminar |
L2 |
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Tue, 19/05/2009 17:00 |
Dave Benson (University of Aberdeen) |
Algebra Seminar |
L2 |
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Tue, 26/05/2009 17:00 |
Pham Tiep (University of Florida) |
Algebra Seminar |
L2 |
| Many classical results and conjectures in representation theory of finite groups (such as theorems of Thompson, Ito, Michler, the McKay conjecture, ...) address the influence of global properties of representations of a finite group G on its p-local structure. It turns out that several of them also admit real, resp. rational, versions, where one replaces the set of all complex representations of G by the much smaller subset of real, resp. rational, representations. In this talk we will discuss some of these results, recently obtained by the speaker and his collaborators. We will also discuss recent progress on the Brauer height zero conjecture for 2-blocks of maximal defect. | |||
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Tue, 02/06/2009 17:00 |
Michael Aschbacher (Caltech) |
Algebra Seminar |
L2 |
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Tue, 09/06/2009 17:00 |
Michael Collins (Oxford) |
Algebra Seminar |
L2 |
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Tue, 16/06/2009 17:00 |
Mikhail Ershov (University of Virginia) |
Algebra Seminar |
L2 |
| Informally speaking, a finitely generated group G is said to be Golod-Shafarevich (with respect to a prime p) if it has a presentation with a “small” set of relators, where relators are counted with different weights depending on how deep they lie in the Zassenhaus p-filtration. Golod-Shafarevich groups are known to behave like (non-abelian) free groups in many ways: for instance, every Golod-Shafarevich group G has an infinite torsion quotient, and the pro-p completion of G contains a non-abelian free pro-p group. In this talk I will extend the list of known “largeness” properties of Golod-Shafarevich groups by showing that they always have an infinite quotient with Kazhdan's property (T). An important consequence of this result is a positive answer to a well-known question on non-amenability of Golod-Shafarevich groups. | |||
