Conference on Progress in PDE 9–13 July
2001 Scientific Organising Committee: John Ball (Oxford),
Alexander Grigoryan (Imperial College), Sergei Kuksin (HeriotWatt)
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 longterm benefit to all the participants.
The core of the meeting
was the series of keynote lectures delivered by worldleaders 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 wellposedness of nonlinear
dispersive equations 
V A Kondratiev: 
Secondorder 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 
ST 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 surveytalk 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 spacevariable and when the solution is a
vectorfunction of a onedimensional space variable. The second group of
results was recently completed by the speaker and his collaborators, so his
talk presented the most upto 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 vectorfields 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
nonlinear dispersive equation. Many of the results were obtained by the
speaker himself. Nikolai Nadirashsili reviewed recent highlights in the theory
of nonlinear 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
NavierStokes equations via model problems which catch various essential
features of the NavierStokes dynamics. A classical exponent of modern theory
of PDEs, Professor Mark Vishik, spoke on the theory of attractors for
nonlinear evolutionary PDEs, both autonomous and nonautonomous.
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 citycentre.
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 –
HeriotWatt 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 – TECHNIONIsrael Institute of Technology
Caillol, Philippe – University of Loughborough Carlsson, Ulf
– Institution for Matematik, KTH Carr, Jack – HeriotWatt
University Cherednichenko, Kirill – University of Bath Chmaj, Adam
– HeirotWatt University Coulhon, Thierry – Université de
CergyPontoise De Lellis, Camillo – Scuola Normale Superiore di Pisa
De Pauw, Thierry – Université de ParisSud (Orsay) Dekkers,
Sophia – Imperial College London Dull, WolfPatrick –
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 – HeriotWatt
University Kenig, Carlos – University of Chicago Kinnunen, Juha
– Helsinki University of Technology Knops, Robin – HeriotWatt
University Kokarev, Gerasim – HeriotWatt University Kondratiev,
Vladimir – Moscow State University Kosmodem’yanskii, A. –
MIIT Kotani, Motoko – Tohoku University Krylov, Nicolai –
University of Minnesota Kuksin, Sergei – HeriotWatt 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
CergyPontoise Levitin, Michael – HeriotWatt 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, Sunra –
Scuola Normale Superiore Müller, Stefan – MaxPlanck 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 – MaxPlanck Institute
Selden, Jeffrey – University of Arizona Setti, Alberto G. –
Università dell’InsurbiaComo Shargorodsky, Eugene –
University of Sussex Shirikyan, Armen – HeriotWatt 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 –
MaxPlanck 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, ShingTung –
Harvard University Zhang, Yanping – HeriotWatt University
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