Algebra Seminar (past)
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Tue, 26/01/2010 17:00 |
Nikolai Nikolov (Imperial College London) |
Algebra Seminar  |
L2 |
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Tue, 19/01/2010 17:00 |
Paul Lescot (University of Rouen) |
Algebra Seminar |
L2 |
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Tue, 01/12/2009 00:00 |
Martin Bridson (Oxford) |
Algebra Seminar |
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Tue, 24/11/2009 17:00 |
Tim Burness (Southampton) |
Algebra Seminar |
L2 |
| Let G be a permutation group on a set S. A base for G is a subset B of S such that the pointwise stabilizer of B in G is trivial. We write b(G) for the minimal size of a base for G. Bases for finite permutation groups have been studied since the early days of group theory in the nineteenth century. More recently, strong bounds on b(G) have been obtained in the case where G is a finite simple group, culminating in the recent proof, using probabilistic methods, of a conjecture of Cameron. In this talk, I will report on some recent joint work with Bob Guralnick and Jan Saxl on base sizes for algebraic groups. Let G be a simple algebraic group over an algebraically closed field and let S = G/H be a transitive G-variety, where H is a maximal closed subgroup of G. Our goal is to determine b(G) exactly, and to obtain similar results for some additional base-related measures which arise naturally in the algebraic group context. I will explain the key ideas and present some of the results we have obtained thus far. I will also describe some connections with the corresponding finite groups of Lie type. | |||
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Tue, 17/11/2009 17:00 |
Vincent Franjou (Nantes) |
Algebra Seminar |
L2 |
| A classic problem in invariant theory, often referred to as Hilbert's 14th problem, asks, when a group acts on a finitely generated commutative algebra by algebra automorphisms, whether the ring of invariants is still finitely generated. I shall present joint work with W. van der Kallen treating the problem for a Chevalley group over an arbitrary base. Progress on the corresponding problem of finite generation for rational cohomology will be discussed. | |||
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Tue, 10/11/2009 17:00 |
Colva Roney-Dougal (St Andrews) |
Algebra Seminar |
L2 |
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Tue, 03/11/2009 17:00 |
Anne Thomas (Oxford) |
Algebra Seminar |
L2 |
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Tue, 27/10/2009 17:00 |
Michael Wemyss (Oxford) |
Algebra Seminar |
L2 |
| I'll explain how the `Auslander philosophy' from finite dimensional algebras gives new methods to tackle problems in higher-dimensional birational geometry. The geometry tells us what we want to be true in the algebra and conversely the algebra gives us methods of establishing derived equivalences (and other phenomenon) in geometry. Algebraically two of the main consequences are a version of AR duality that covers non-isolated singularities and also a theory of mutation which applies to quivers that have both loops and two-cycles. | |||
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Tue, 20/10/2009 17:00 |
Kobi Kremnizer (Oxford) |
Algebra Seminar |
L2 |
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Tue, 13/10/2009 17:00 |
Aner Shalev (Jerusalem) |
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. | |||
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Tue, 09/06/2009 17:00 |
Michael Collins (Oxford) |
Algebra Seminar |
L2 |
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Tue, 02/06/2009 17:00 |
Michael Aschbacher (Caltech) |
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, 19/05/2009 17:00 |
Dave Benson (University of Aberdeen) |
Algebra Seminar |
L2 |
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Tue, 12/05/2009 17:00 |
Erika Damian (University of East Anglia) |
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, 28/04/2009 17:00 |
Peter Fiebig (Universitat Freiburg) |
Algebra Seminar |
L2 |
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Tue, 10/03/2009 17:00 |
Gunter Malle (University of Kaiserslautern) |
Algebra Seminar |
L2 |
| We classify certain linear representations of finite groups with a large orbit. This is motivated by a question on the number of conjugacy classes of a finite group. | |||
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Tue, 03/03/2009 17:00 |
Markus Linckelmann (University of Aberdeen) |
Algebra Seminar |
L2 |
