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Algebra Seminar (past)

Tue, 30/11/2010
17:00 		Tatiana Bandman (Bar-Ilan) Algebra Seminar Add to calendar L2
Geometry and dynamics of some word maps on SL(2, Fq)
I will speak about a geometric method, based on the classical trace map, for investigating word maps on groups PSL(2, q) and SL(2, q). In two different papers (with F. Grunewald, B. Kunyavskii, and Sh. Garion, F. Grunewald, respectively) this approach was applied to the following problems. 1. Description of Engel-like sequences of words in two variables which characterize finite solvable groups. The original problem was reformulated in the language of verbal dynamical systems on SL(2). This allowed us to explain the mechanism of the proofs for known sequences and to obtain a method for producing more sequences of the same nature. 2. Investigation of the surjectivity of the word map defined by the n-th Engel word [[[X, Y ], Y ], . . . , Y ] on the groups PSL(2, q) and SL(2, q). Proven was that for SL(2, q), this map is surjective onto the subset SL(2, q) $ \setminus $ {−id} $ \subset $ SL(2, q) provided that q $ \ge q_0(n) $ is sufficiently large. If $ n\le 4 $ then the map was proven to be surjective for all PSL(2, q).
Tue, 23/11/2010
17:15 		Panos Papazoglou (Oxford) Algebra Seminar Add to calendar L2
Quasi-isometry invariance of splittings and the lamplighter group
Tue, 16/11/2010
17:00 		Raphaël Rouquier (Oxford) Algebra Seminar Add to calendar L2
Finite generation of group cohomology
Tue, 09/11/2010
17:00 		Olivier Dudas (Oxford) Algebra Seminar Add to calendar L2
Brauer trees of finite reductive groups
Tue, 02/11/2010
17:00 		Nikolay Nikolov (Imperial College) Algebra Seminar Add to calendar L2
Product decompositions of simple groups
Tue, 26/10/2010
17:00 		Algebra Seminar Add to calendar L2
No seminar
Tue, 19/10/2010
17:00 		Desi Kochloukova (UNICAMP) Algebra Seminar Add to calendar L2
Homological finiteness Bredon properties for groups
We discuss homological finiteness Bredon types FPm with respect to the class of finite subgroups and seperately with respect to the class of virtually cyclic subgroups. We will concentrate to the case of solubles groups and if the time allows to the case of generalized R. Thompson groups of type F. The results announced are joint work with Brita Nucinkis (Southampton) and Conchita Martinez Perez (Zaragoza) and will appear in papers in Bulletin of LMS and Israel Journal of Mathematics.
Tue, 12/10/2010
17:00 		Kevin McGerty (Oxford) Algebra Seminar Add to calendar L2
Duality for representations and quantum isogenies
Recently Frenkel and Hernandez introduced a kind of "Langlands duality" for characters of semisimple Lie algebras. We will discuss a representation-theoretic interpretation of their duality using quantum analogues of exceptional isogenies. Time permitting we will also discuss a branching rule and relations to Littelmann paths.
Tue, 15/06/2010
17:00 		Detlev Hoffmann (Nottingham) Algebra Seminar Add to calendar L2
Bilinear Forms and Differential Forms under Field Extensions
An important problem in algebra is the study of algebraic objects defined over fields and how they behave under field extensions, for example the Brauer group of a field, Galois cohomology groups over fields, Milnor K-theory of a field, or the Witt ring of bilinear forms over a field. Of particular interest is the determination of the kernel of the restriction map when passing to a field extension. We will give an overview over some known results concerning the kernel of the restriction map from the Witt ring of a field to the Witt ring of an extension field. Over fields of characteristic not two, general results are rather sparse. In characteristic two, we have a much more complete picture. In this talk, I will explain the full solution to this problem for extensions that are given by function fields of hypersurfaces over fields of characteristic two. An important tool is the study of the behaviour of differential forms over fields of positive characteristic under field extensions. The result for Witt rings in characteristic two then follows by applying earlier results by Kato, Aravire-Baeza, and Laghribi. This is joint work with Andrew Dolphin.
Tue, 08/06/2010
17:00 		Yiftach Barnea (Royal Holloway) Algebra Seminar Add to calendar L2
Abstract Commensurators of Profinite Groups
Tue, 01/06/2010
17:00 		Peter Jorgensen (Newcastle) Algebra Seminar Add to calendar L2
The cluster category of Dynkin type $ A_\infty $
   The cluster category of Dynkin type $ A_\infty $ is a ubiquitous object with interesting properties, some of which will be explained in this talk.
   Let us denote the category by $ \mathcal{D} $. Then $ \mathcal{D} $ is a 2-Calabi-Yau triangulated category which can be defined in a standard way as an orbit category, but it is also the compact derived category $ D^c(C^{∗}(S^2;k)) $ of the singular cochain algebra $ C^*(S^2;k) $ of the 2-sphere $ S^{2} $. There is also a “universal” definition: $ \mathcal{D} $ is the algebraic triangulated category generated by a 2-spherical object. It was proved by Keller, Yang, and Zhou that there is a unique such category.
  Just like cluster categories of finite quivers, $ \mathcal{D} $ has many cluster tilting subcategories, with the crucial difference that in $ \mathcal{D} $, the cluster tilting subcategories have infinitely many indecomposable objects, so do not correspond to cluster tilting objects.
   The talk will show how the cluster tilting subcategories have a rich combinatorial structure: They can be parametrised by “triangulations of the $ \infty $-gon”. These are certain maximal collections of non-crossing arcs between non-neighbouring integers.
  This will be used to show how to obtain a subcategory of $ \mathcal{D} $ which has all the properties of a cluster tilting subcategory, except that it is not functorially finite. There will also be remarks on how $ \mathcal{D} $ generalises the situation from Dynkin type $ A_n $ , and how triangulations of the $ \infty $-gon are new and interesting combinatorial objects.
Tue, 25/05/2010
17:00 		Emmanuel Breuillard (Université de Paris-Sud, Orsay) Algebra Seminar Add to calendar L2
Variations on the Tits alternative(s)
Tue, 18/05/2010
17:00 		Martin Bridson (Oxford) Algebra Seminar Add to calendar L2
Actions of higher-rank lattices on free groups
Tue, 11/05/2010
17:00 		Peter Cameron (Queen Mary University) Algebra Seminar Add to calendar L2
Power graphs of groups and other magmas
Tue, 27/04/2010
17:00 		Andrei Marcus (Cluj) Algebra Seminar Add to calendar L2
Hopf-Galois extensions and an exact sequence for H-Picard groups
The topic of this talk is the representation theory of Hopf-Galois extensions. We consider the following questions. Let H be a Hopf algebra, and A, B right H-comodule algebras. Assume that A and B are faithfully flat H-Galois extensions. 1. If A and B are Morita equivalent, does it follow that the subalgebras A^coH and B^coH of H-coinvariant elements are also Morita equivalent? 2. Conversely, if A^coH and B^coH are Morita equivalent, when does it follow that A and B are Morita equivalent? As an application, we investigate H-Morita autoequivalences of the H-Galois extension A, introduce the concept of H-Picard group, and we establish an exact sequence linking the H-Picard group of A and the Picard group of A^coH.(joint work with Stefaan Caenepeel)
Tue, 09/03/2010
17:00 		Andrzej Zuk (Paris VII Denis Diderot) Algebra Seminar Add to calendar L2
Zero divisors in von Neumann algebras
Tue, 02/03/2010
17:00 		Pierre Cartier (IHES) Algebra Seminar Add to calendar L2
On the field with one element
Tue, 23/02/2010
17:00 		Pierre-Emmanuel Caprace (Universite catholique de louvain) Algebra Seminar Add to calendar L2
Commensurators of profinite wreath branch groups
Tue, 16/02/2010
17:00 		John Duncan (Cambridge) Algebra Seminar Add to calendar L2
Monstrous moonshine and black holes
   In 1939 Rademacher derived a conditionally convergent series expression for the modular j-invariant, and used this expression—the first Rademacher sum—to verify its modular invariance. We may attach Rademacher sums to other discrete groups of isometries of the hyperbolic plane, and we may ask how the automorphy of the resulting functions reflects the geometry of the group in question.
   In the case of a group that defines a genus zero quotient of the hyperbolic plane the relationship is particularly striking. On the other hand, of the common features of the groups that arise in monstrous moonshine, the genus zero property is perhaps the most elusive. We will illustrate how Rademacher sums elucidate this phenomena by using them to formulate a characterization of the discrete groups of monstrous moonshine.
  A physical interpretation of the Rademacher sums comes into view when we consider black holes in the context of three dimensional quantum gravity. This observation, together with the application of Rademacher sums to moonshine, amounts to a new connection between moonshine, number theory and physics, and furnishes applications in all three fields.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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