# Special Session:

Analysis

Organizers: David Preiss (Warwick) and Ray Ryan (NUI, Galway)
This special session is followed by the Operator Theory and Real Analysis Splinter Group on both afternoons.

## Tuesday, April 7 2009

14:15 - 15:10

*Cairnes Lecture Theatre*
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Ivan Todorov (Queen's University Belfast):

Stable isomorphism of dual operator spaces

Two dual operator spaces X and Y are said to be stably isomorphic if the dual operator spaces
obtained from X and Y after tensoring with
the space B(H) of all bounded operators on a Hilbert space H
are completely isometric and weak* homeomorphic.
The notion of stable isomorphism, which is coarser than that of
isomorphism, is closely related to the notion of Morita equivalence.
In this talk, we present necessary and sufficient conditions
for stable isomorphism of two dual operator spaces
in terms of ternary rings of operators, that is, operator spaces closed under
the triple product (a,b,c)\rightarrow ab^*c. We describe some
applications of the results to the theory of dual operator algebras
and present some examples motivated by the theory of CSL algebras.

15:15 - 16:10 *Cairnes Lecture Theatre*

###
Marianna Csőrnyei (UC London):

Differentiability of Lipschitz functions and other problems in geometric measure theory

Our main goal in this talk is to describe non-differentiability
sets of Lipschitz functions on {\mathbb R}^n. This will lead us to the
notion of tangent fields to null sets, and provide a new understanding of
the structure of sets of small measure. This is a joint work with G.
Alberti and D. Preiss.

## Wednesday, April 8 2009

14:15 - 15:10

*Cairnes Lecture Theatre*
###
Stephen Gardiner (UCD):

Harmonic functions outside a cylinder

Several apparently different problems have recently led to
consideration of harmonic functions in the complement of an infinite
cylinder. It turns out that, in three dimensions, estimates for the
Dirichlet problem and the Green function in this context are quite
delicate. This talk will describe the motivation for studying such
questions as well as definitive answers.

15:15 - 16:10 *Cairnes Lecture Theatre*

###
Richard Haydon (University of Oxford):

On the scalar-plus-compact problem

A problem that has been open for some time is whether there
exists a Banach space on which every bounded linear operator has the form
\lambda I + K with \lambda a scalar and K a compact operator. The
talk will discuss the background to the problem, and its recent solution
by S.A. Argyros and the speaker.