Partial Differential Equations
Overview
Partial Differential Equations is a large subject with a history that dates back to Newton and Leibniz. They form the basis for many mathematical models in the sciences and in economics, yielding such famous equations as the Euler and Navier Stokes equations and Schrodinger's and Einstein's equations. Moreover the subject is far more that just a mathematical tool to address physical and economic phenomena; PDE's have guided and created the fields of nonlinear functional analysis, harmonic analysis, optimization and the modern calculus of variations, and have had a major impact on the field of geometry. The later, was recently highlighted by the role of Ricci flow in the eventual proof of the celebrated Poincare Conjecture.
This diversity is reflected in the research of many faculty members across the PIMS universities and this Collaborative Research Group will provide the means for:
 Bringing together faculty from different PIMS universities with both clearly defined, and not so clearly defined common research interests, and encouraging collaborations between these groups.
 Bringing in several postdoctoral fellows, creating critical masses at the various PIMS sites.
 Sponsoring graduate and post doctoral courses and minicourses which will provide access to a wide audience at PIMS universities. Currently there is not the critical mass to offer such course at the majority of PIMS universities.
Focus
The CRG on PDE will focus on several key areas (both for training and research):
 Geometry and analysis of dispersive equations
 Regularity for solutions of certain fundamental equations (NavierStokes, harmonic measures, the infinity Laplacian)
 The role of hyperbolic problems in traffic flow, kinetic theory and the material sciences
 Modern approaches to asymptotic analysis in the calculus of variations and applications
 general variational principles
 Universal inequalities in relevant function spaces
 The role of game theory and stochastic methods in certain elliptic and parabolic equations
Faculty
Participating Faculty from PIMS Universities
 UBC  Ivar Ekeland, Antoine Mellet, Nassif Ghoussoub, Stephen Gustafson, TaiPeng Tsai, Richard Froese
 SFU  Rustum Choksi, Adam Oberman, Razvan Fetecau, JF Williams
 UVic  Reinhard Illner Martial Agueh Boualem Khouider Chris Bose
 UCalgary  Christian Rios
 UW  Gunther Uhlmann, Hart Smith
Activities
 Mar 30Apr 04, 2008 at BIRS, Recent Developments in Elliptic and Degenerate Elliptic Partial Differential Equations, Systems and Geometric Measure Theory Organizers: David CruzUribe (Trinity College), Steven Hofmann (University of MissouriColumbia), Marius Mitrea (University of Missouri, Columbia), Salvador Perez Esteva (Universidad Nacional Au tonoma de Mexico), Cristian Rios (University of Calgary), Eric Sawyer (McMaster University).
 June 2008, UBC Workshop on the NashMoser implicit function theorem and its applications in the calculus of variations Organizers: I. Ekeland (UBC), Florin Diacu (UVic)
 April 27May 2, 2008 at BIRS, Nonlocal operators and applications. Organizers: Cyril Imbert (University ParisDauphine, CEREMADE), Antoine Mellet (University of British Columbia), Regis Monneau (ENPC).
 Aug 24Aug 29, 2008 at BIRS, Asymptotics and Singularities in Nonlinear and Geometric Dispersive Equations Organizers: Zeng Chongchun (Georgia Tech.), Stephen Gustafson (University of British Columbia), Kenji Nakanishi (Kyoto University), TaiPeng Tsai (University of British Columbia).
 Minisymposium in PDE at PIMSUBC, November 1213, 2009
 Pacific Northwest Conferences

Victoria (September 2008) Organizers: R. Illner. M. Agueh.

UBC (January 17, 2009) Organizers: R. Froese, N. Ghoussoub.

 Seminars

PDE/Geometry/Math Physics seminar at UBC (S. Gustafson)

PDE seminar at SFU (R. Choksi)

PDE seminar at UVic (R. Illner)

PDE seminar at Calgary (C. Rios)

PDE seminar at Alberta (W. Allegretto)

PDE seminar at Washington (G. Uhlmann)

Visitors and Special Lectures
PIMS Postdoctoral Fellows:
 Yves van Gennip (Simon Fraser University), 20082010
 Mohammad El Smaily (University of British Columbia), 20082010
 Vianney Combet (University of British Columbia), 20102012
 Diego Ribeiro Moreira (University of British Columbia), 20102012
 Ian Zwiers (University of British Columbia), 20102012
PIMS Distinguished Visitors:
 Selim Esedoglu (Michigan) visiting SFU and UBC on January 1624, 2009
 Wilfrid Gangbo (Georgia Tech) visiting UBC on January 1518, 2009
 Changfeng Gui (Connecticut) visiting UBC on January 819, 2009
 Nader Masmoudi (Courant Institute) visiting UBC
 David Kinderlehrer, Carnegie Mellon University visiting UVic from Sept 24, 2008 to Sept 27, 2008 and then UBC until Oct 1, 2008.
Prof. ChangShou Lin, Department of Mathematics, National Taiwan University, visiting UBC from Sept 11, 2008 to Sept 15, 2008.
Name  Affiliation  Arrival  Departure 
Hakan Andreasson  University of Gothenburg  June 27  July 4 
Anton Arnold  Vienna University of Technology  June 21  July 7 
Andrea Braides  Universita degli Study di Roma Tor Vergata  July 6  July 13 
Yann Brenier  UniversitÃ© de NiceSophie Antipolis  July 19  August 11 
Luis Caffarelli  University of Texas at Houston  July 20  July 24 
Pierre Cardaliaguet  UniversitÃ© de Brest  July 19  July 29 
Antonin Chambolle  Ã‰cole Polytechnique  July 19  July 31 
StÃ©phane Cordier  UniversitÃ© d'OrlÃ©ans  June 28  July 5 
Francesca Da Lio  University of Padova  July 17  July 24 
Pierre Degond  Centre National de la Recherche Scientifique (CNRS)  July 17  July 24 
Jose Carrillo de la Plata  Universitat AutÃ²noma de Barcelona  June 28  July 17 
Nicolas Dirr  University of Bath  July 18  July 25 
Jean Dolbeault  UniversitÃ© Paris Dauphine  June 21  July 17 
Italo Capuzzo Dolcetta  UniversitÃ Roma La Sapienza  July 18  July 24 
Pierpaolo Esposito  UniversitÃ degli Studi Roma Tre  July 5  July 25 
Klemens Fellner  University of Cambridge  June 27  July 5 
Irene Fonseca  University of Minnesota  July 5  July 9 
MiHo Giga  University of Tokyo  July 22  August 7 
Changfeng Gui  University of Connecticut  July 1  August 1 
Cyril Imbert  UniversitÃ© ParisDauphine  July 18  July 24 
Hitoshi Ishii  WASEDA University  July 20  July 25 
Robert Jensen  Loyola University Chicago  July 24  August 1 
Robert Jerrard  University of Toronto  July 5  July 11 
Ansgar Jungel  Vienna University of Technology  June 21  July 3 
Petri Juutinen  University of JyvÃ¤skylÃ¤  July 25  July 31 
Bernd Kawohl  University of Cologne  July 12  August 1 
Robert Kohn  New York University  July 26  July 31 
Andrea Malchiodi  SISSA  July 5  July 10 
Simona Mancini  UniversitÃ© d'OrlÃ©ans  June 28  July 5 
Juan Jose Manfredi  University of Pittsburgh  July 26  August 1 
Florian Mehats  UniversitÃ© de Rennes 1  June 21  July 9 
Luc Mieussens  UniversitÃ© Bordeaux 1  June 27  July 3 
Robert Mills Strain III  Princeton University  June 21  August 8 
Phil Morrison  University of Texas  June 21  July 3 
Stefan MÃ¼ller  Max Planck Institute for Mathematics in the Sciences  July 6  July 10 
Barbara Niethammer  University of Oxford  July 4  July 11 
James Nolen  Duke University  July 18  July 25 
Frank Pacard  UniversitÃ© Paris 12  July 4  July 11 
Mark Peletier  Technische Universiteit Eindhoven  July 5  July 10 
Yuval Peres  University of California Berkeley  July 26  July 29 
Arshak Petrosyan  Purdue University  July 19  July 24 
Tristan RiviÃ¨re  Swiss Federal Institute of Technology (ETH)  July 4  July 24 
Frederic Robert  UniversitÃ© de Nice SophiaAntipolis  July 5  July 21 
Russell Schwab  University of Texas at Austin  July 18  July 25 
Eric SÃ©rÃ©  UniverisitÃ© Paris Dauphine  July 5  July 11 
Sylvia Serfaty  Courant Institute of Mathematical Sciences  July 27  July 31 
Scott Sheffield  MIT  July 27  July 31 
Henrik Shahgholian  KTH Royal Institute of Technology  July 20  July 23 
Yannick Sire  UniversitÃ© Paul CÃ©zanne  July 19  July 24 
P.E. Souganidis  University of Chicago  July 20  July 24 
Peter Sternberg  Indiana University  July 6  July 10 
Vitali Vougalter  University of Toronto  June 28  July 4 
Jack Xin  University of KÃ¶ln  July 19  July 22 
Yifeng Yu  University of Texas at Austin  July 18  August 1 
Andrej Zlatos  University of Chicago  July 19  July 26 
Reinhard Illner  University of Victoria  Nov 12  Nov 13 
Ben Stephens  University of Washington  Nov 9  Nov 14 
Andrea Bertozzi  UCLA  Nov 12  Nov 13 