NEWS
2001/2002
Issue No 11

2001 SCIENTIFIC PROGRAMME

Conference on Progress in PDE
9–13 July 2001

Scientific Organising Committee:
John Ball (Oxford),
Alexander Grigoryan (Imperial College),
Sergei Kuksin (Heriot-Watt)

Supported by:
The Engineering and Physical Sciences Research Council, the European Commission (Framework 5)

The goal of the conference was to bring together those researchers who define progress in PDE research and to organise a series of lectures on current progress and problems of long-term benefit to all the participants.

The core of the meeting was the series of keynote lectures delivered by world-leaders in this area of research. The talks, in alphabetical order, were as follows:

A Bressan: Viscosity solutions for hyperbolic systems of conservation laws
B Engquist: On the Prandtl boundary layer equation
G Forni: Cohomological equations, invariant distributions and ergodic theory
E Grenier: Stability of boundary layers through Green’s functions
C Kenig: Recent progress in the well-posedness of non-linear dispersive equations
V A Kondratiev: Second-order semilinear elliptic equations in unbounded domains
N Krylov: The heat equation in Lq ((0,T ), Lp ) spaces with weights
A Kupiainen: Ergodic properties of 2d turbulence
S Müller: Solving nonlinear PDE by linear algebra
N Nadirashvili: New results and open problems in elliptic PDE
F Otto: Scaling laws and interpolation inequalities
V Sverák: On simple models of the Navier- Stokes equations
N Trudinger: On the affine maximal surface equation
M Vishik: Trajectories and global attractors for equations in mathematical physics
S-T Yau: Eigenvalues and the existence of black holes
In addition, there were four sessions of shorter contributed talks and, on Tuesday, a special session dedicated to the memory of E M Landis, addressing qualitative theory of second order elliptic and parabolic PDEs.

All participants had an opportunity to present a poster and the Organisers also selected 12 people (including younger researchers) to give a short talk.
The meeting web pages contain full details of the main talks, including in many cases abstracts and notes from the main speakers. See www.icms.org.uk/current/progpde/index.html

A brief summary of some of the speakers follows.

Alberto Bressan gave a survey-talk on viscosity solutions for hyperbolic equations. The theory is now developed for two classes of problems: when the solution is a scalar function of a multidimensional space-variable and when the solution is a vector-function of a one-dimensional space variable. The second group of results was recently completed by the speaker and his collaborators, so his talk presented the most up-to date state of affairs in the field. Giovanni Forni gave a talk on his research on the frontier of PDEs and dynamical systems. He discussed hypoelliptic properties of the operators differentiating along certain vector-fields on a compact manifold and their relations with qualitative properties of some dynamical systems. Charles Kenig gave an excellent survey on recent progress in the theory of generalised solutions for non-linear dispersive equation. Many of the results were obtained by the speaker himself. Nikolai Nadirashsili reviewed recent highlights in the theory of non-linear elliptic equations and their applications in differential geometry. An important component of his talk was the presentation of a list of carefully chosen open problems in the field and their discussion. Vladimir Sverák discussed progress and failures in the programme to study 3D Navier-Stokes equations via model problems which catch various essential features of the Navier-Stokes dynamics. A classical exponent of modern theory of PDEs, Professor Mark Vishik, spoke on the theory of attractors for non-linear evolutionary PDEs, both autonomous and non-autonomous.

The Conference was held in the Royal Society of Edinburgh, and the majority of participants stayed at Pollock Halls, a little to the east of the city-centre. Although the full timetable left only a short period for discussion during the day, the participants were encouraged to make use of the facilities at ICMS for informal discussion in the breaks and early evenings.

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Participants

Ball, John – University of Oxford
Barbatis, Gerassimos – University of Crete
Bevan, Jonathan – University of Oxford
Bila, Nicoleta – University of Kent at Canterbury
Biryuk, Andrei – Heriot-Watt University
Bland, John – University of Toronto
Blocki, Zbigniew – Jagiellonian University
Bocea, Marian – Carnegie Mellon University
Boulton, L – King’s College London
Bournaveas, Nikolaos – University of Edinburgh
Bressan, Alberto – SISSA
Brooks, Robert – TECHNION-Israel Institute of Technology
Caillol, Philippe – University of Loughborough
Carlsson, Ulf – Institution for Matematik, KTH
Carr, Jack – Heriot-Watt University
Cherednichenko, Kirill – University of Bath
Chmaj, Adam – Heirot-Watt University
Coulhon, Thierry – Université de Cergy-Pontoise
De Lellis, Camillo – Scuola Normale Superiore di Pisa
De Pauw, Thierry – Université de Paris-Sud (Orsay)
Dekkers, Sophia – Imperial College London
Dull, Wolf-Patrick – Universität Bonn
Dutrifoy, Alexandre – Université Libre de Bruxelles
Engquist, Bjorn – UCLA
Fakhi, Saadia – Université de Paris XII
Fei, Ning – Heriot Watt University
Forni, Giovanni – Princeton University
Friedlander, Leonid – University of Arizona
Garcia Leon, Joel – Imperial College
Grenier, Emmanuel – Ecole Normale Superieure de Lyon
Grigor’yan, Alexander – Imperial College
Grunewald, Natalia – Institüt fur Angewandte Mathematik
Gyongy, Istvan – Edinburgh University
Hoang, Viet Ha – University of Cambridge
Holopainen, Ilkka – University of Helsinki
Hui, Kin Ming – Academia Sinica
Ibragimov, Akif – Texas A&M University
Jefferson, Daniel – Heriot-Watt University
Kenig, Carlos – University of Chicago
Kinnunen, Juha – Helsinki University of Technology
Knops, Robin – Heriot-Watt University
Kokarev, Gerasim – Heriot-Watt University
Kondratiev, Vladimir – Moscow State University
Kosmodem’yanskii, A. – MIIT
Kotani, Motoko – Tohoku University
Krylov, Nicolai – University of Minnesota
Kuksin, Sergei – Heriot-Watt University
Kupiainen, Antti – University of Helsinki
Labutin, Denis – Swiss Federal Institute of Technology, Zurich
Lerena, Maria Belen – Universidad Complutense de Madrid
Levin, Daniel – Université de Cergy-Pontoise
Levitin, Michael – Heriot-Watt University
Liskevich, Vitali – University of Bristol
Lopes Filho, Milton – UNICAMP
Lorent, Andrew – University of Jyvaskyla
Mascarenhas, M.L. – University of Lisbon
Miao, Changxing – University of Coventry
Micallef, Mario – University of Warwick
Moroz, Vitaly – University of Bristol
Mosconi, Sun-ra – Scuola Normale Superiore
Müller, Stefan – Max-Planck Institute for Mathematics
Nadirashvili, Nikolai – University of Chicago
O’Donnell, Peter – Anglia Polytechnic University
Otto, Felix – Universitat Bonn
Petursson, Ingi – University of Warwick
Piatnitski, Andrey – Lebedev Physical Inst RAS (& Narvik Uni, Norway)
Pigola, Stefano – Università degli Studi di Milano
Pons, Daniel – Imperial College
Rebah, Dirar – Unviersity of Bath
Renclawowicz, Joanna – Polish Academy of Sciences
Rossovskii, Leonid – Moscow State Aviation Institute
Ruzhansky, Michael – Imperial College
Schloemerkemper, Anja – Max-Planck Institute
Selden, Jeffrey – University of Arizona
Setti, Alberto G. – Università dell’Insurbia-Como
Shargorodsky, Eugene – University of Sussex
Shirikyan, Armen – Heriot-Watt University
Skubachevskii, A. – Moscow State Aviational Institute
Sobol, Zeev – University of Bielefeld
Stroffolini, Bianca – University of Naples
Sugimoto, Mitsuru – Imperial College
Sverák, Vladimir – University of Minnesota at Minneapolis
Taheri, Ali – Max-Planck Institute for Mathematics
Tertikas, Achilles – University of Crete
Trudinger, Neil – Australian National University
Vanneste, Jacques – University of Edinburgh
Vishik, Mark – Institute for Transmission Problems
von Renesse, Max – University of Bonn
Yan, Guozheng – University of Coventry
Yau, Shing-Tung – Harvard University
Zhang, Yanping – Heriot-Watt University

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