UK and Republic of Ireland SIAM Section Annual Meeting

 	     Held 7th January, 2005 in Cork.


This was the first annual meeting of the section held in the 
Republic of Ireland and coincided with the opening of Cork as
European City of Culture. Despite the rain and wind there was an 
excellent turnout for the meeting at the University College Cork (UCC).

The first speaker was Neil O' Connell (Warwick) who gave an informative
survey talk on random matrices. Starting with some applications of random
matrices including telephone encryption he examined the distribution of
eigenvalues of random (orthogonal and unitary) matrices.  By analogy with
electrostatics he explained why the eigenvalues are more regularly spaced than
might be expected. An open puzzle is a phase transition in the distribution of
eigenvalues of powers of unitary matrices. Finally it was explained how 
eigenvalues of random unitary matrices are closely related, in a statistical 
sense, to the zeros of the Riemann zeta function.

Niall O Murchadha (UCC) gave an entertaining talk 
on the degrees of freedom of the gravitational field as specified by the
equations of General Relativity, an appropriate topic in the centenary year 
of 3 of Einstein's seminal publications. He made extensive use of the analogy
with the Maxwell equations of the electromagnetic field to show the
necessity of splitting the equations into constraint and evolution
parts. His talk placed the research in historical context, and showed how 
it underlies current efforts in numerical relativity. 
A question regarding the well-posedness of the evolution equations provided 
further opportunity for the speaker to demonstrate his enthusiasm for this 
fascinating subject, and to highlight the difficulty of outstanding research 
challenges.


After lunch Ivan Graham (Bath) described efficient boundary element
methods (BEMs) for PDEs. Typical applications such as computing
electrostatic capacitance and acoustic obstacle scattering were presented.
This clear and interesting talk contrasted the BEM to a standard finite
element or finite difference method and surveyed some recent results on
complexity issues. Mathematical challenges were presented, such as those
arising from the treatment of irregular boundaries.  It was shown how,
with an appropriate fast matrix vector multiplication method, the
complexity of the BEM was  competitive with that of a FEM. Recent research
which extend the methods and analysis to degenerate meshes was
summarised.

Russell Davies (Aberystwyth) gave an interesting talk on wobble, creep
and relaxation where he is modelling materials with memory. He enthusiastically
explained that what constitutes a fluid depends on the time scale of the
observations : including sagging tombstones and mountains flowing. He
talked on the corkscrew instability that arises in extrusion of plastics
or similar visco-elastic flows. He then asked why a jelly wobbles. The
answer, in terms of mathematics, was given as a Sturm-Liouville problem.
An open question, of relevance to the industrial processing of all polymeric
materials, is to determine the dominant rate of decay of the transient.

The final speaker, Alexei Pokrovskii (UCC), introduced equations with 
hysteresis nonlinearities. He used computer applets to illustrate 
the important rate-independent property of hysteresis, which cannot 
be easily described in terms of standard mathematical formulas. The 
Krasnoselskii program for investigating hysteresis was outlined, and 
stress was laid upon the Identification Theorem, which links many types 
of hysteresis behaviour to the Preisach operator. The lecture concluded 
with an overview of some recent results on the complicated behaviour of 
a pendulum subject to hysteresis, including a rigorous proof of the existence 
of chaos.


Business meeting : This was held after an excellent lunch.
^^^^^^^^^^^^^^^^

The UKIE section president, Martin Stynes, gave a brief overview of the 
past year and reminded the members present that the posts of President 
and Vice-President become vacant at the end of March 2005 and nominations for
were solicited. The secretary reported on finances and activities funded in 
the year including the 5 student prizes presented. It was generally agreed 
that these activities should be continued and if possible extended. 

The meeting thanked Trevor Stuart and Andy Wathen for their hard work in 
trying to arrange a joint meeting with the LMS, IMA, CMS and SIAM in the UK 
which unfortunately fell through. It was agreed that there is still strong 
interest in UKIE SIAM in holding SIAM Conferences either the UK or 
Republic of Ireland. Andy Wathen noted that SIAM will be holding the 2005 
SIAM Conference on Optimization in Stockholm and if that goes well further 
meetings outside the US may occur. He also noted that the European 
representatives on Board and Council were always willing to raise any points 
members might have.  

In answer to some specific points raised at the meeting.
*) The UKIE section is linked from http://www.siam.org/sectchapt/sections.htm
*) The meeting appeared on http://www.siam.org/meetings/calendar.htm

The next annual meeting will be in January 2006, preferably Jan 6, 
venue to be decided.

James Gleeson and Gabriel Lord