Algebra Seminar
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Tue, 03/05/2011 17:00 |
Prof. Aner Shalev (Jerusalem) |
Algebra Seminar  |
L2 |
| Word maps on groups were studied extensively in the past few years, in connection to various conjectures on profinite groups, finite groups, finite simple groups, etc. I will provide background, as well as very recent works (joint with Larsen, Larsen-Tiep, Liebeck-O'Brien-Tiep) on word maps with relations to representations (e.g. Gowers' method and character ratios), geometry and probability. Recent applications, e.g. to subgroup growth and representation varieties, will also be described. I will conclude with a list of problems and conjectures which are still very much open. The talk should be accessible to a wide audience. | |||
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Tue, 10/05/2011 17:00 |
Dr Aditi Kar (Southampton) |
Algebra Seminar |
L2 |
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Tue, 17/05/2011 17:00 |
Dr Khalid Bou-Rabee (Michigan) |
Algebra Seminar |
L2 |
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In 1939, Wilhelm Magnus gave a characterization of free groups in terms of their rank and nilpotent quotients. Our goal in this talk is to present results giving both positive and negative answers to the following question: does a similar characterization hold within the class of finite-extensions of finitely generated free groups? This talk covers joint work with Brandon Seward.
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Tue, 24/05/2011 17:00 |
Prof. V. Bavula (Sheffield) |
Algebra Seminar |
L2 |
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In 1968, Dixmier posed six problems for the algebra of polynomial differential operators, i.e. the Weyl algebra. In 1975, Joseph solved the third and sixth problems and, in 2005, I solved the fifth problem and gave a positive solution to the fourth problem but only for homogeneous differential operators. The remaining three problems are still open. The first problem/conjecture of Dixmier (which is equivalent to the Jacobian Conjecture as was shown in 2005-07 by Tsuchimito, Belov and Kontsevich) claims that the Weyl algebra `behaves' like a finite field. The first problem/conjecture of Dixmier: is it true that an algebra endomorphism of the Weyl algebra an automorphism? In 2010, I proved that this question has an affirmative answer for the algebra of polynomial integro-differential operators. In my talk, I will explain the main ideas, the structure of the proof and recent progress on the first problem/conjecture of Dixmier.
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Tue, 31/05/2011 17:00 |
Prof. Goulnara Arjantseva (Vienna) |
Algebra Seminar |
L2 |
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Tue, 14/06/2011 17:00 |
Benno Kuckuck (Oxford) |
Algebra Seminar |
L2 |
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Direct products of finitely generated free groups have a surprisingly rich subgroup structure. We will talk about how the finiteness properties of a subgroup of a direct product relate to the way it is embedded in the ambient product. Central to this connection is a conjecture on finiteness properties of fibre products, which we will present along with different approaches towards solving it. |
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