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DEPARTMENT
of MATHEMATICS
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Saturday January 10 - Sunday January 11, 2004
Chancellors Hotel and Conference Centre, University of ManchesterA workshop New Frontiers in Computational Mathematics with 63 participants was held January 10 and 11, 2004 at the Chancellors Hotel and Conference Centre, University of Manchester. It was organized by Nick Higham, Tony Shardlow, Fran\c{c}oise Tisseur (University of Manchester) and David Silvester (UMIST) under the auspices of the Manchester Centre for Computational Mathematics, with financial support from the University of Manchester, The London Mathematical Society, the UK and Republic of Ireland SIAM section, the Royal Society and the Wolfson Foundation. The workshop focused on four cutting edge, interdisciplinary research areas of computational mathematics, with each area having a keynote speaker and other contributed talks and posters. Just the briefest highlights are reported here. For more details, see the conference web site (http://www.maths.man.ac.uk/MCCM/frontiers.html), which contains links to many of the presentations.
Jack Dongarra (University of Tennessee, Knoxville and Oak Ridge National Laboratory) opened the workshop with a talk "Trends in High Performance Computing and the Grid" in which he discussed the evolution of computational power and how it is measured, and showed how the power is being exploited in diverse computational applications ranging from grid computing to Google. Mikel Lujan (University of Manchester) described how the OoLaLa project is using object technology in the design of high performance linear algebra libraries, in order to reduce the number of specialized interfaces, and hence the coding effort, while having minimal impact on performance. Len Freeman (University of Manchester) described a feedback-guided parallel loop scheduling algorithm that was motivated by a collaboration with the UK Meteorological Office.
A diverse session on mathematical biology was opened by Mark Chaplain (University of Dundee), with a fascinating survey of the modelling of cancer cells, and particularly angiogenesis, by describing the evolution of networks of blood vessels. Of interest both for the mathematics and the insight into the workings of our bodies, this session also offered a computational study of airway closure by Andrew Hazel (University of Manchester), (one of the conclusions: keep breathing!), computational models of pattern formation on butterfly wings from Andrew Wathen (Oxford University), and work on the little studied "mathematical modelling of micturation" by urologist C. P. Arun (University College, London). Arun gets the award for the most striking title: "Bladder contraction is rocket science!".
Per Christian Hansen (Technical University of Denmark) lead the session on inverse problems and ill-posed problems, with a talk "Large-Scale Methods for Linear Inverse Problems". Via numerous practical examples, he emphasized the importance of regularization and the advantages of exploiting structure in large-scale problems. Also in this session, Bill Lionheart (UMIST) discussed inverse problems in electromagnetics, including electrical impedance tomography in medical diagnosis, and described a number of interesting PDE and optimization problems that arise.
The final session on image processing and computer vision was opened by Tony Chan (UCLA), who discussed partial differential equation methods. He treated, among many other things, the "inpainting" problem of filling in an occluded subject in an image---something of interest to all those of us whose thumb tends to get in front of our camera lens without us noticing it until after the picture is taken. Ke Chen (Liverpool) discussed multigrid techniques for solving the PDEs of imaging. Stephen Marsland (University of Manchester), explained the advantages of using diffeomorphisms in image registration, illustrating with the geodesic clamped spline and examples drawn from brain scans.
A notable feature of the meeting was the high standard of the 18 posters, which were professionally produced and very readable.
Overlapping with this meeting was a one and a half day workshop celebrating the 60th birthdays of numerical analysts Jim Varah, Alan George, and Michael Saunders, held at Stanford University, January 9-10, 2004 and organized by Gene Golub (Stanford), Michael Friedlander (Argonne National Laboratory), Chen Greif (University of British Columbia), and Esmond Ng (Lawrence Berkeley National Laboratory). Written greetings from attendees at the New Frontiers meeting were faxed across to Stanford, including best wishes for many more productive years.
In his concluding remarks, David Silvester remarked that this workshop had delimited the frontiers of knowledge in the four areas of computational mathematics considered---an ample result for a weekend's work---and that he hoped that a future more lengthy Manchester workshop would *extend* the boundaries.