Algebra Seminar
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Tue, 24/04/2007 17:00 |
Dr. Corneliu Hoffman (Birmingham) |
Algebra Seminar  |
L1 |
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Tue, 01/05/2007 17:00 |
Dr. Nikolay Nikolov (Oxford/Imperial) |
Algebra Seminar |
L1 |
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Tue, 08/05/2007 17:00 |
Prof. Bernard Leclerc (Caen) |
Algebra Seminar |
L1 |
| Let G be a complex semisimple algebraic group of type A,D,E. Fomin and Zelevinsky conjecture that the coordinate rings of many interesting varieties attached to G have a natural cluster algebra structure. In a joint work with C. Geiss and J. Schroer we realize part of this program by introducing a cluster structure on the multi-homogeneous coordinate ring of G/P for any parabolic subgroup P of G. This was previously known only for P = B a Borel (Berenstein-Fomin-Zelevinsky) and when G/P is a grassmannian Gr(k,n) (J. Scott). We give a classification of all pairs (G,P) for which this cluster algebra has finite type. Our construction relies on a finite-dimensional algebra attached to G, the preprojective algebra introduced in 1979 by Gelfand and Ponomarev. We use the fact that the coordinate ring of the unipotent radical of P is "categorified" in a natural way by a certain subcategory of the module category of the preprojective algebra. | |||
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Tue, 15/05/2007 17:00 |
Algebra Seminar |
L1 | |
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Tue, 22/05/2007 17:00 |
Dr Martin Bridson (Imperial College, London) |
Algebra Seminar |
L1 |
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Tue, 29/05/2007 17:00 |
Dr. Ben Klposch (Royal Holloway) |
Algebra Seminar |
L1 |
| I will talk about some ongoing work, motivated by a long standing problem in the theory of dynamical systems. In particular, I will explain how p-adic methods lead to the construction of elements in SL_n(Z) whose eigenvalues e_1, ., e_n generate a free abelian subgroup of rank n-1 in the multiplicative group of positive real numbers. This is a special instance of a more general theorem, asserting the existence of strongly hyperbolic elements in arithmetic subgroups of SL_n(R). | |||
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Tue, 05/06/2007 17:00 |
Prof. R. Grigorchuk (Texas A&M) |
Algebra Seminar |
L1 |
| We will speak about the problem of classification of self-similar groups. The main focus will be on groups generated by three-state automata over an alphabet on two letters. Numerous examples will be presented, as well as some results concerning this class of groups. | |||
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Tue, 12/06/2007 17:00 |
Prof. Takeshi Suzuki (Okayama) |
Algebra Seminar |
L1 |
