Issue No 11


Instructional Conference Nonlinear Partial Differential Equations
8–18 January 2001

Scientific Organising Committee:
John Ball (Oxford),
Maria Esteban (Paris),
John Toland (Bath)

Supported by: European Commission (Framework V), Engineering and Physical Sciences Research Council, and The London Mathematical Society

This Instructional Conference (the latest in a series of such meetings organised by ICMS) took the form of a demanding two-week course on current research in nonlinear PDE. It concentrated on the most widely used and applicable techniques, such as variational methods and the maximum principle, and on applications in a variety of scientific contexts at a quite sophisticated level. The Organisers aimed to provide a series of lecture courses, in each of which a single speaker had an opportunity to present a overview of a topic in lectures delivered over a few days. The format gives the young researchers the chance to digest and discuss what had been said.

The courses were graded, with the more basic material presented in the first week. The lecturers, from centres of excellence all over Europe, were leading experts in their areas, and put a great deal of effort (that was much appreciated) into the preparation of courses and individual lectures.

The Conference began with an introductory course by Geoffrey Burton on nonlinear functional analysis and function spaces. Modern techniques in the calculus of variations were covered by Charles Stuart and Jan Kristensen and Maria Esteban, and John Ball explained applications to mathematical chemistry and to the microstructure of materials. Luigi Ambrosio began with an introduction to geometric measure theory and went on to discuss variational problems which arise in image processing and fracture mechanics. Maximum principles were treated in the course by Amadine Aftalion.

These technique-oriented courses were followed by lectures on a number of more specialised topics with other applications in mind. The participants heard from Yann Brenier on problems of fluid and plasma dynamics, from Claude Le Bris on variational models of atoms, molecules and crystals, and from Vincent Caselles on PDE in static and dynamic image processing. Finally there were individual lectures by Alfio Quarteroni on mathematical models of blood flow, by John Toland on water waves, and by Norman Dancer on peak solutions of elliptic equations. A lecture by Nizar Touzi (Sorbonne) on mathematics in finance was planned but, despite pressure from the Organisers, he was unable to obtain a UK entry visa.

The majority of young researchers attended for both weeks. Lectures in the first week should have greatly enhanced their understanding of the more advanced material presented in the second week.

The instructional lectures were all 90 minutes long, allowing time for questions during and after the talks, and many of the speakers prepared handouts that were available to all participants.

The meeting attracted participants of at least 12 nationalities, including a group of postgraduate and postdoctoral students from the USA. Most speakers and younger researchers stayed on the Heriot-Watt Campus where there was ample opportunity for interaction at all levels. It seems that very few knew each other before attending, so the Organisers felt confident that new networks were formed that would enrich future research careers.

In the UK the PDE curriculum is not so well developed as it is in other countries, and the courses were much appreciated by young local mathematicians for the exposure they offered to basic material. For participants from other countries, such as France, Italy and Germany where PDEs are heavily studied, the Conference was valuable not only for the quality of the international speakers who were available for discussion, but also for the strong theme of important and challenging examples that nowadays motivate many important innovations, some of which were discussed during the meeting.

In spite of the demands made by the introduction of so much mathematics in such a short time, it was remarkable how attendance at the courses remained high throughout.

The participants should have been left with a strong impression of the importance and utility of the theory of nonlinear partial differential equations in basic science and in a variety of areas with key economic significance, for example, medicine or materials science.

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Aftalion, Amadine – Université Paris 6
Ainsworth, Mark – Strathclyde University
Ambrosio, Luigi – Scuola Normale Superiore
Baia, Margarida – Carnegie Mellon
Ball, John – University of Oxford
Biryuk, Andrei – Heriot-Watt University
Blanc, Xavier – Ecole Nationale des Ponts et Chaussees
Bocea, Marian – Carnegie Mellon University
Bortoloni, Luca – University of Bologna
Brenier, Yann – CNRS Université de Nice
Buica, Adriana – Babes-Bolyai University of Cluj- Napoca
Burton, Geoffrey – University of Bath
Caselles, Vicent – Universitat Pompeu Fabra
Catarino, Nuno – University of Warwick
Crooks, Elaine – University of Oxford
Dancer, Norman – University of Sydney
Davies, Penny – University of Strathclyde
Esteban, Maria – Université Paris IX – Dauphine
Faraco, Daniel – University of Jyvaskyla
Fei, Ning – Heriot-Watt University
Gaio, Ana – University of Warwick
Gauthier, Alain – University of Strathclyde
He, Xinyu – University of Warwick
Knops, Robin – Heriot-Watt University
Kokarev, Gerasim – Heriot-Watt University
Kristensen, Jan – Heriot-Watt University
Le Bris, Claude – Ecole Nationale des Ponts et Chaussees
Mackay, Cameron – Strathclyde University
Matthies, Karsten – University of Oxford
McMillan, Ewen – University of Oxford
Melcher, Christof – Max-Planck Institute
Mulholland, Anthony – Strathclyde University
Nardone, Mario – University of Padova
Olofsson, Anders – University of Stockholm
Pavliotis, Grigorios – Rensselaer Polytechnic Institute
Popovici, Cristina – Carnegie Mellon University
Quarteroni, Alfio – EPF Lausanne
Radu, Petronela – Carnegie Mellon University
Rodriguez, Jose Antonio – Leiden University
Rothos, Vassilis – Loughborough University
Ruzhansky, Michael – Imperial College, London
Sansalone, Vittorio – Universita ‘Roma Tre’
Santos, Pedro – Carnegie Mellon University
Schloemerkemper, Anja – Max-Planck Institute
Singer, Michael – University of Edinburgh
Stoleriu, Iulian – University of Strathclyde
Stuart, Charles – Ecole Polytechnique Federale de Lausanne
Szekelyhidi, Laszlo – Max-Planck Institute
Toland, John – University of Bath
Trudinger, Neil – Australian National University
Vani, Cheruvu – Indian Institute of Technology, Madras
Vernaeve, Hans – University of Gent
Vuillaume, Gregory – EPF Lausanne
Waddell, Chris – University of Strathclyde
Zappale, Elvira – Carnegie Mellon University
Zhang, Yanping – Heriot-Watt University

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