The program is still to be confirmed, but will consist of twoandahalf days of postgraduate and invited talks, with poster presentations another option.
This year
we will have invited talks by established Mathematicians in this field.
For a more detailed program and list of talks, please see the
attached PDF.
See also:
Participants
Wednesday

12:00  12:30 
Introductions 
Department Coffee Room (G/109) 
12:30  14:00 
Lunch 

14:00  15:00 
Invited Speaker: Steve Power (Lancaster)
Crystal Frameworks and Rigidity Operators

ADS/106 
15:00  17:30 
Session 1 (break at 16:00) 
ADS/106 
Thursday

09:00  12:30 
Session 2 (break at 11:00) 
ADS/106 
12:30  14:00 
Lunch 

14:00  15:00 
Invited Speaker: Michael Dritschel (Newcastle)
A Tour of von Neumann's Inequality

ADS/106 
15:00  17:30 
Session 3 (break at 16:00) 
ADS/106 
20:00 
Conference Dinner 
TBC 
Friday

09:00 11:30

Session 4 (break at 11:00) 
ADS/106 
11:30  12:30

Invited Speaker: Simon Eveson (York)
The Strange Ubiquity of Rank 1 
ADS/106 
12:30  14:00 
Lunch 

14:00  15:30 (provisional) 
Session 4 and end of workshop 
ADS/106 
Abstracts
Apologies for the raw LaTeX markup in some abstracts; please see the PDF for a formatted version.
Invited Talks
Michael Dritschel (Newcastle)
A Tour of von Neumann's Inequality
In 1951 John von Neumann published the following inequality which bears
his name:
If $p$ is a complex polynomial and $T$ is a bounded Hilbert space
operator with $\T\ \leq 1$, then $\p(T)\ \leq \p\_\infty$, the
supremum norm of $p$ over the unit disk.
The inequality has immediate application to functional calculus
questions, and for this reason (among others) it is interesting to know
for which function algebras and operators inequalities of this sort are
attained.
For example, given a function algebra $\mathcal A$ over a
complex domain with norm denoted by $\\cdot\_\infty$ (though perhaps
not the supremum norm!), one could look for conditions on an operator
$T$ such that $f(T)$ makes sense for $f\in A$ and $\f(T)\ \leq
\f\_\infty$.
Or one might also ask: given a collection of operators, are there natural domains and function algebras over these domains such
that some version of von Neumann's inequality holds?
What about
algebras over $\mathbb C^n$ or tuples of operators (commuting or not)?
We will touch on many of these problems, discuss some of the recent work
in this area, list a few of the many applications and point to open
problems around this fascinating inequality.
Simon Eveson (York)
The Strange Ubiquity of Rank 1
The
simplest linear operators on a Banach space are those of rank 1. This
talk describes three different situations in which relatively
complicated linear systems exhibit very simple rank 1 behaviour in an
asymptotic sense. This leads to a question (to which I don't know the
answer!): are these isolated examples, or part of some more general
theory?
Steve Power (Lancaster)
Crystal Frameworks and Rigidity Operators
A finite barjoint framework in three dimensions has an associated rigidity matrix which detects infinitesimal rigidity and flexibility of the framework.
Infinite barjoint (bondnode) frameworks, with periodic structure, play a role in mathematical models for Rigid Unit mode vibrations (low energy phonons) in material crystals.
I shall introduce their infinite rigidity matrices and rigidity operators and present some of the foundations of a fledgling topic.
In particular I hope to indicate,
 how one may compute the rigid unit mode spectrum of a crystal framework, and
 how one might develop a Hilbert space theory for "square summable flexes".