15 October 2013

17:00

15 October 2013

17:00

15 October 2013

(All day)Konstantin Ardakov

Abstract

Affinoid enveloping algebras arise as certain p-adic completions of ordinary enveloping algebras, and are closely related to Iwasawa algebras. I will explain how to use Beilinson-Bernstein localisation to compute their (non-commutative) Krull dimension. This is recent joint work with Ian Grojnowski.

11 June 2013

17:00

Benjamin Klopsch

Abstract

4 June 2013

17:00

Alexey Sevastyanov

Abstract

<p>Let g be the complex semisimple Lie algebra associated to a complex semisimple algebraic group G, b a Borel subalgebra of g, h the Cartan sublagebra contained in b and N the unipotent subgroup corresponding to the nilradical n of b. Extremal projection operators are projection operators onto the subspaces of n-invariants in certain g-modules the action of n on which is locally nilpotent. Zhelobenko also introduced a family of operators which are analogues to extremal projection operators. These operators are called now Zhelobenko operators.<br />I shall show that the explicit formula for the extremal projection operator for g obtained by Asherova, Smirnov and Tolstoy and similar formulas for Zhelobenko operators are related to the existence of a birational equivalence (N, h) -> b given by the restriction of the adjoint action. Simple geometric proofs of formulas for the ``classical'' counterparts of the extremal projection operator and of Zhelobenko operators are also obtained.</p>

28 May 2013

17:00

Yves Cornulier

Abstract

We will first recall the known notion of commensurating actions
and its link to actions on CAT(0) cube complexes. We define a
group to have Property FW if every isometric action on a CAT(0)
cube complex has a fixed point. We conjecture that every
irreducible lattice in a semisimple Lie group of higher rank has
Property FW, and will give some instances beyond the trivial
case of Kazhdan groups.

28 May 2013

15:30

Michael Bate

Abstract

21 May 2013

17:00

Anreas Doering

Abstract

The spectral presheaf of a nonabelian von Neumann algebra or C*-algebra
was introduced as a generalised phase space for a quantum system in the
so-called topos approach to quantum theory. Here, it will be shown that
the spectral presheaf has many features of a spectrum of a
noncommutative operator algebra (and that it can be defined for other
classes of algebras as well). The main idea is that the spectrum of a
nonabelian algebra may not be a set, but a presheaf or sheaf over the
base category of abelian subalgebras. In general, the spectral presheaf
has no points, i.e., no global sections. I will show that there is a
contravariant functor from unital C*-algebras to their spectral
presheaves, and that a C*-algebra is determined up to Jordan
*-isomorphisms by its spectral presheaf in many cases. Moreover, time
evolution of a quantum system can be described in terms of flows on the
spectral presheaf, and commutators show up in a natural way. I will
indicate how combining the Jordan and Lie algebra structures may lead to
a full reconstruction of nonabelian C*- or von Neumann algebra from its
spectral presheaf.

14 May 2013

17:00

Brita Nucinkis

Abstract

7 May 2013

(All day)Andreas Doring

Abstract

<p>The spectral presheaf of a nonabelian von Neumann algebra or C*-algebra was introduced as a generalised phase space for a quantum system in the so-called topos approach to quantum theory. Here, it will be shown that the spectral presheaf has many features of a spectrum of a noncommutative operator algebra (and that it can be defined for other classes of algebras as well). The main idea is that the spectrum of a nonabelian algebra may not be a set, but a presheaf or sheaf over the base category of abelian subalgebras. In general, the spectral presheaf has no points, i.e., no global sections. I will show that there is a contravariant functor from unital C*-algebras to their spectral presheaves, and that a C*-algebra is determined up to Jordan *-isomorphisms by its spectral presheaf in many cases. Moreover, time evolution of a quantum system can be described in terms of flows on the spectral presheaf, and commutators show up in a natural way. I will indicate how combining the Jordan and Lie algebra structures may lead to a full reconstruction of nonabelian C*- or von Neumann algebra from its spectral presheaf.</p>

30 April 2013

17:00

Elizaveta Frenkel

Abstract

In my talk I shall give a small survey on some algorithmic properties of amalgamated products of finite rank

free groups. In particular, I'm going to concentrate on Membership Problem for this groups. Apart from being algorithmically interesting, amalgams of free groups admit a lot of interpretations. I shall show how to

characterize this construction from the point of view of geometry and linguistic.