Algebra Seminar
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Tue, 13/10/2009 17:00 |
Aner Shalev (Jerusalem) |
Algebra Seminar  |
L2 |
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Tue, 20/10/2009 17:00 |
Kobi Kremnizer (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, 03/11/2009 17:00 |
Anne Thomas (Oxford) |
Algebra Seminar |
L2 |
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Tue, 10/11/2009 17:00 |
Colva Roney-Dougal (St Andrews) |
Algebra Seminar |
L2 |
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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, 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, 01/12/2009 00:00 |
Martin Bridson (Oxford) |
Algebra Seminar |
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