Forthcoming Seminars › Seminar Series

Algebra Seminar

Tue, 15/01/2008
16:00 		Jochen Koenigsmann (Oxford) Algebra Seminar Add to calendar L1
Higher Galois Theory between arithmetic, logic and geometry
Tue, 22/01/2008
16:00 		Idun Reiten (Trondheim) Algebra Seminar Add to calendar L1
Cluster-tilted algebras and quivers with potentials
Tue, 29/01/2008
16:00 		Peter Pappas (Vassar/Oxford) Algebra Seminar Add to calendar L1
On the Unit Conjecture for Group Rings
Tue, 05/02/2008
16:00 		Toby Stafford (Manchester) Algebra Seminar Add to calendar L1
Cherednik algebras, Hilbert schemes and quantum hamiltonian reduction
Cherednik algebras (always of type A in this talk) are an intriguing class of algebras that have been used to answer questions in a range of different areas, including integrable systems, combinatorics and the (non)existence of crepant resolutions. A couple of years ago Iain Gordon and I proved that they form a non-commutative deformation of the Hilbert scheme of points in the plane. This can be used to obtain detailed information about the representation theory of these algebras. In the first part of the talk I will survey some of these results. In the second part of the talk I will discuss recent work with Gordon and Victor Ginzburg. This shows that the approach of Gordon and myself is closely related to Gan and Ginzburg's quantum Hamiltonian reduction. This again has applications to representation theory; for example it can be used to prove the equidimensionality of characteristic varieties.
Tue, 12/02/2008
16:00 		Cornelia Drutu (Oxford) Algebra Seminar Add to calendar L1
Embeddings of families of rescaled graphs into Cayley graphs, examples of groups with exotic properties
I shall explain two ways of embedding families of rescaled graphs into Cayley graphs of groups. The first one allows to construct finitely generated groups with continuously many non-homeomorphic asymptotic cones (joint work with M. Sapir). Note that by a result of Shelah, Kramer, Tent and Thomas, under the Continuum Hypothesis, a finitely generated group can have at most continuously many non-isometric asymptotic cones. The second way is less general, but it works for instance for families of Cayley graphs of finite groups that are expanders. It allows to construct finitely generated groups with (uniformly convex Banach space)-compression taking any value in [0,1], and with asymptotic dimension 2. In particular it gives the first example of a group uniformly embeddable in a Hilbert space with (uniformly convex Banach space)-compression zero. This is a joint work with G. Arzhantseva and M.Sapir.
Tue, 26/02/2008
16:00 		Derek Holt (Warwick) Algebra Seminar Add to calendar L1
Maximal subgroups of finite groups
Tue, 04/03/2008
16:00 		Alex Muranov (Lyon) Algebra Seminar Add to calendar L1
Boundedly generated groups and small-cancellation method
A group is called boundedly generated if it is the product of a finite sequence of its cyclic subgroups. Bounded generation is a property possessed by finitely generated abelian groups and by some other linear groups. Apparently it was not known before whether all boundedly generated groups are linear. Another question about such groups has also been open for a while: If a torsion-free group $ G $ has a finite sequence of generators $ a_1,\dotsc,a_n $ such that every element of $ G $ can be written in a unique way as $ a_1^{k_1}\dotsm a_n^{k_n} $, where $ k_i\in\mathbb Z $, is it true then that $ G $ is virtually polycyclic? (Vasiliy Bludov, Kourovka Notebook, 1995.) Counterexamples to resolve these two questions have been constructed using small-cancellation method of combinatorial group theory. In particular boundedly generated simple groups have been constructed.

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

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