**1:15 to 2:15****2:30 to 3:30****3:30 to 4:00****4:00 to 5:00****6:00**

Niels Laustsen: On finitely-generated, maximal left ideals of operators acting on a Banach space

Abstract: I shall report on an ongoing joint research project with Garth Dales, Tomasz Kania (both Lancaster) and Piotr Koszmider (IMPAN, Warsaw) in which we study the finitely-generated, maximal left ideals of the Banach algebra B(E) of bounded, linear operators acting on a Banach space E. More precisely, we consider the following two questions for an infinite-dimensional Banach space E:

(I) Does B(E) necessarily contain a maximal left ideal which is not finitely generated?

(II) Is every finitely-generated, maximal left ideal of B(E) necessarily of the form {T in B(E) : Tx = 0} for some non-zero element x of E? Since the two-sided ideal F(E) of finite-rank operators is not contained in any of the maximal left ideals considered in (II), a positive answer to Question (II) would imply a positive answer to Question (I). For this reason, it seems natural to also consider the following, formally more specific, variant of Question (II):

(III) Is F(E) ever contained in a finitely-generated, maximal left ideal of B(E)?

However, Questions (II) and (III) turn out to be equivalent (in the sense that (II) has a positive answer if and only if (III) has a negative answer). We answer Question (I) in the positive for a large number of Banach spaces, and conjecture that the answer is always positive. In contrast, we show that Question (II) has a positive answer for some, but not all, Banach spaces.

Zinaida Lykova: Topologically pure extensions of Frechet algebras and applications to homology

Abstract: The class of topologically pure extensions of Frechet and Banach algebras is larger than the class of splittable extensions. For example, any extension of C*-algebras is topologically pure. At the same time they allow circumvention of the known problem that the projective tensor product of injective continuous linear operators is not necessarily injective. We use them to establish the excision property in the cyclic continuous (co)homology and a Kuenneth formula in topological homology. We describe explicitly the continuous Hochschild and cyclic cohomology groups of certain topological algebras. We describe explicitly the continuous Hochschild and cyclic cohomology groups of certain topological algebras.

Tea

Joachim Zacharias: Constructing spectral triples on C*-algebras

Abstract: We discuss the construction spectral triples and quantum metric spaces on various C*-algebras in particular crossed products.

Dinner