Algebra Seminar
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Tue, 18/01/2011 17:00 |
Prof. J. S. Wilson (Oxford) |
Algebra Seminar  |
L2 |
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Tue, 25/01/2011 17:00 |
Prof. D. Segal (Oxford) |
Algebra Seminar |
L2 |
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Tue, 01/02/2011 17:00 |
Dr David Stewart (Oxford) |
Algebra Seminar |
L2 |
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Tue, 08/02/2011 17:00 |
Dr Ehud Meir (Newton Institute) |
Algebra Seminar |
L2 |
| Abstract: this is joint work with Eli Aljadeff. Let G be a group, H a finite index subgroup. Moore's conjecture says that under a certain condition on G and H (which we call the Moore's condition), a G-module M which is projective over H is projective over G. In other words- if we know that a module is “almost projective”, then it is projective. In this talk we will survey cases in which the conjecture is known to be true. This includes the case in which the group G is finite and the case in which the group G has finite cohomological dimension. As a generalization of these two cases, we shall present Kropholler's hierarchy LHF, and discuss the conjecture for groups in this hierarchy. In the case of finite groups and in the case of finite cohomological dimension groups, the conjecture is proved by the same finiteness argument. This argument is straightforward in the finite cohomological dimension case, and is a result of a theorem of Serre in case the group is finite. We will show that inside Kropholler's hierarchy the conjecture holds even though this finiteness condition might fail to hold. We will also discuss some other cases in which the conjecture is known to be true (e.g. Thompson's group F). | |||
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Tue, 15/02/2011 17:00 |
Prof. Martin Liebeck (Imperial) |
Algebra Seminar |
L2 |
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Tue, 22/02/2011 17:00 |
Lars Louder (Oxford) |
Algebra Seminar |
L2 |
| I will prove that generating sets of surface groups are either reducible or Nielsen equivalent to standard generating sets, improving upon a theorem of Zieschang. Equivalently, Aut(F_n) acts transitively on Epi(F_n,S) when S is a surface group. | |||
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Tue, 01/03/2011 17:00 |
Prof. Martin Kassabov (Southampton) |
Algebra Seminar |
L2 |
| We analyze the question of the minimal index of a normal subgroup in a free group which does not contain a given element. Recent work by BouRabee-McReynolds and Rivin give estimates for the index. By using results on the length of shortest identities in finite simple groups we recover and improve polynomial upper and lower bounds for the order of the quotient. The bounds can be improved further if we assume that the element lies in the lower central series. | |||
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Tue, 08/03/2011 17:00 |
Dr Chloé Perin (Strasbourg) |
Algebra Seminar |
L2 |
| Following the works of Sela and Kharlampovich-Myasnikov on the Tarski problem, we are interested in the first-order logic of free (and more generally hyperbolic) groups. It turns out that techniques from geometric group theory can be used to answer many questions coming from model theory on these groups. We showed with Sklinos that free groups of finite rank are homogeneous, namely that two tuples of elements which have the same first-order properties are in the same orbit under the action of the automorphism group. We also show that this is not the case for most surface groups. | |||
