Forthcoming events in this series


Tue, 27 May 2008

17:00 - 18:00
L1

On polyzeta values

Olivier Mathieu
(Université Lyon I)
Tue, 22 Apr 2008

17:00 - 18:00
L1

Totally Disconnected, Locally Compact Groups & Geometric Group Theory

Udo Baumgartner
(Newcastle)
Abstract

As a small step towards an understanding of the relationship of the two fields in the title, I will present a uniformness result for embeddings of finitely generated, virtually free groups as cocompact, discrete subgroups in totally disconnected, locally compact groups.

Tue, 04 Mar 2008

16:00 - 17:00
L1

Boundedly generated groups and small-cancellation method

Alex Muranov
(Lyon)
Abstract

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.

Tue, 12 Feb 2008

16:00 - 17:00
L1

Embeddings of families of rescaled graphs into Cayley graphs, examples of groups with exotic properties

Cornelia Drutu
(Oxford)
Abstract

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, 05 Feb 2008

16:00 - 17:00
L1

Cherednik algebras, Hilbert schemes and quantum hamiltonian reduction

Toby Stafford
(Manchester)
Abstract

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, 20 Nov 2007

16:00 - 17:00
L1

On Engel groups

Prof. M. Vaughan-Lee
(Oxford)
Tue, 05 Jun 2007
17:00
L1

The beginning of the Atlas of self-similar groups

Prof. R. Grigorchuk
(Texas A&M)
Abstract

 

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.

 

Tue, 29 May 2007
17:00
L1

Anosov diiffeomorphisms and strongly hyperbolic elements in arithmetic subgroups of SL_n(R)

Dr. Ben Klposch
(Royal Holloway)
Abstract

 

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).