## Information

We plan a meeting to be held in the new Research visitors centre in the School of Mathematics, University of Leeds. The format of the meeting will be that of a "working semester", in the broad area of Banach Algebras, and Operator Spaces, as applied to topological groups (to include locally compact groups, other topological groups, and the operator algebra approach to quantum groups). During the meeting there will be two conferences and a series of instructional lectures.

## Programme

The *provisional programme* is as follows.

#### Monday 17 May 2010

Start of the programme: welcome meeting at **11am in the MALL.**

#### Thursday 27 May -- Saturday 29 May

#### 6-12 June

International Functional Analysis Meeting in Valencia: We expect that many participants will travel to Spain for this meeting. There are some travel hints.

#### Monday 28 June -- Wednesday 30 June

#### Wednesday 30 June

Official end of the programme

## Conferences

There will be two conferences held during the meeting, the first one on the 27, 28 and 29 May, and the second on the 28, 29 and 30 June. Both are supported by an London Mathematics Society Scheme 1 grant. In particular, there is funding available for Postgraduate students.

Please see the conference page for further details

## Lecture programme

Some of our speakers have had last minute commitments arise, so there have been a few changes, and perhaps a couple of lectures are still subject to being moved.

Downloadable schedule: In Excel Format, In PDF Format.

### Zhong-Jin Ruan

**Monday 17 May, 2pm-3pm**Introduction to operator spaces, duality, examples to include group C*-algebras/von Neumann algebras and Fourier algebras. Slides from lecture**Tuesday 18 May, 11am-noon**Operator amenability of the Fourier algebra. Slides from lecture**Wednesday 19 May, 11am-noon**Approximation properties for C*-algebras and operator spaces. Slides from lecture**Thursday 20 May, 11am-noon**Local properties of group C*-algebras. Slides from lecture**Friday 21 May, 11am-noon**Extensions to the quantum setting. Slides from lecture

### Allan Sinclair

**Wednesday 19 May, 2-3pm**Length for C*-algebras: an introduction: Click for abstract. Slides from lectures

### Alexander Helemskii

Further details on "Extreme flatness and Hahn-Banach type theorems for normed modules over c_0"

**Thursday 20 May, 2pm--3:30pm****Friday 21 May, 2pm--3:30pm**

### Zhiguo Hu

**Monday 24 May, 11am-noon**Banach algebras with an algebraic structure of Kakutani-Kodaira flavour; some applications. Slides from lecture**Tuesday 25 May, 11am-noon**Topological centres and SIN quantum groups. Slides from lecture**Wednesday 26 May, 11am-noon**Quotient strong Arens irregularity over locally compact quantum groups and some related problems.

### Adam Skalski

**Monday 24 May, 2pm-3pm**Actions of compact quantum groups: deﬁnition of actions, notion of continuity/nondegeneracy, invariant states, ergodicity, categories of quantum groups or semigroups acting on a given C*-algebra and preserving some additional structure. Slides from lecture**Tuesday 25 May, 2pm-3pm**Quantum symmetry groups of ﬁnite structures: quantum permutation groups, quantum symmetry groups of graphs, Wang and Van Daele’s universal compact quantum groups. Slides from lecture**Wednesday 26 May, 2pm-3pm**Quantum isometry groups of noncommutative manifolds: quantum isometry groups of spectral triples, quantum symmetry groups of Bratteli diagrams and quantum isometry groups associated to group C*-algebras. Slides from lecture

For further details, see PDF abstract.

### Viktor Losert

A survey on results about the multipliers of the Fourier algebra for SL(2,R). To cover notions from representation theory, indicate some technical details and some accompanying results (computation of certain Arens products). Printed notes based upon talk (PDF) and Scanned slides from talks (PDF)

**Monday 31 May, 2pm-3pm and 4pm to 5pm**This is an NBFAS meeting.**Tuesday 1 June, 2pm-3:30pm****Wednesday 2 June, 2pm-3:30pm**

### Volker Runde

The notion of `amenability' for locally compact groups is fundamental; amenability is characterized in many different ways. Here are some characterizations, each in the language of Banach algebras: a locally compact group is amenable if and only if the group algebra L1(G) is amenable if and only if L1(G) is operator amenable if and only if the Fourier algebra A(G) has a bounded approximate identity if and only if A(G) is operator amenable. These lectures will survey to what extent these results generalize to locally compact quantum groups.

**Tuesday 1 June, 10-11am and 11:30am-12:30pm**This is an NBFAS meeting. Slides from 1st talk (Printable version) and Slides from 2nd talk (Printable version).**Wednesday 2 June, 11am-noon**Dual Banach algebras Slides from talk (Printable version).

### Nico Spronk

In 1960 Paul Cohen published a seminal result characterising continuous homomorphisms from commutative group algebras into commutative measure algebras. Various partial generalisations have been given in the meantime, by Greenleaf in 1965 for contractive homomorphisms on non-abelian groups, and by Ilie and Spronk in 2005 in the dual setting of Fourier algebras. Spronk will outline these results and indicate directions for new research, especially concerning compact quantum groups.

**Thursday 3 June, 11am--12:30pm**Slides from talk.**Friday 4 June, 11am--12:30pm**

### Garth Dales

Multi-normed spaces and multi-Banach algebras

The theory of multi-norms was developed by H. G. Dales and M. Polyakov primarily to seek answers to questions that arise in the theory of modules over group algebras. This theory is analogous to, but different from, the theory of operator spaces; it now has something of a life of its own.

The two lectures in the semester will be an introduction to the theory of multi-normed spaces and multi-Banach algebras.

Applications of this theory to the resolution of the mentioned problems involving group algebras will be given in later talks in our semester.

**Thursday 3 June, 2-4pm**Slides from talk.

### Matthew Daws

**Wednesday 16 June, 11am-noon**"Gentle" introduction to group algebras. Talk slides and Printable version.**Thursday 17 June, 11am-noon**Completely bounded multipliers of A(G), and Hilbert C*-modules. Talk slides and Printable version.**Friday 18 June, 11am-noon**Generalisations to locally compact quantum groups. Talk slides and Printable version.

### Pekka Salmi

**Compact quantum subgroups and left invariant C*-subalgebras:**
We discuss compact quantum subgroups of a co-amenable
C*-algebraic quantum group A and their relation to
certain left invariant C*-subalgebras of A.
We show that a compact quantum subgroup of a co-amenable
quantum group is itself co-amenable. As a particular case,
we consider the group C*-algebra of an amenable locally
compact group G: there is a one-to-one correspondence between
open subgroups of G and invariant C*-subalgebras of C*(G).

**Wednesday 16 June, 2-3pm**Slides from talk**Thursday 17 June, 2-3pm**Slides from talk**Friday 18 June, 2-3pm**Slides from talk

### Mathias Neufang

**Tuesday 22 June, 11am-noon**Introduction to locally compact quantum groups, from the Banach algebra perspective.**Wednesday 23 June, 11am-noon**Representation theorems on the ambient space $B(L^2(\G))$**Thursday 24 June, 11am-noon**Harmonic operators and noncommutative Poisson boundaries**Friday 25 June, noon-1pm**Applications: Completely bounded entropy of quantum channels; A functor to groups

### Tom Körner

"Baire Category in Harmonic Analysis". I shall discuss how to use Baire category techniques to obtain results on sets of multiplicity and convolution.

**Tuesday 22 June, 2pm-3pm****Wednesday 23 June, 2pm-3pm****Friday 25 June, 2pm-3pm**

We expect there to be some further lectures given by other participants.

### Wojciech Szymanski

Compact quantum groups: introduction, classification of the C*-algebra given by $SU_q(2)$.

**Thursday 24 June, 4-5pm**

## Register

For the lectures in the semester, there is no formal registration procedure, and no registration fee. This is separate to the conferences. If you plan to attend, then please contact Matthew Daws in the first instance, as we may be able to offer temporary office accommodation. Unfortunately we cannot offer any financial assistance to support attendance at our semester.