Partial Differential Equations

2008 2011


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.


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 (Navier-Stokes, 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


Participating Faculty from PIMS Universities

  • UBC - Ivar Ekeland, Antoine Mellet, Nassif Ghoussoub, Stephen Gustafson, Tai-Peng 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


  • Mar 30-Apr 04, 2008 at BIRS, Recent Developments in Elliptic and Degenerate Elliptic Partial Differential Equations, Systems and Geometric Measure Theory Organizers: David Cruz-Uribe (Trinity College), Steven Hofmann (University of Missouri-Columbia), 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 Nash-Moser implicit function theorem and its applications in the calculus of variations Organizers: I. Ekeland (UBC), Florin Diacu (UVic)
  • April 27-May 2, 2008 at BIRS, Nonlocal operators and applications. Organizers: Cyril Imbert (University Paris-Dauphine, CEREMADE), Antoine Mellet (University of British Columbia), Regis Monneau (ENPC).
  • Aug 24-Aug 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), Tai-Peng Tsai (University of British Columbia).
  • Mini-symposium in PDE at PIMS-UBC, November 12-13, 2009
  • Pacific Northwest Conferences
  • 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), 2008-2010
  • Mohammad El Smaily (University of British Columbia), 2008-2010
  • Vianney Combet (University of British Columbia), 2010-2012
  • Diego Ribeiro Moreira (University of British Columbia), 2010-2012
  • Ian Zwiers (University of British Columbia), 2010-2012

PIMS Distinguished Visitors:

  • Selim Esedoglu (Michigan) visiting SFU and UBC on January 16-24, 2009
  • Wilfrid Gangbo (Georgia Tech) visiting UBC on January 15-18, 2009
  • Changfeng Gui (Connecticut) visiting UBC on January 8-19, 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. Chang-Shou 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 Université de Nice-Sophie Antipolis July 19 August 11
Luis Caffarelli University of Texas at Houston July 20 July 24
Pierre Cardaliaguet Université de Brest July 19 July 29
Antonin Chambolle École Polytechnique July 19 July 31
Stéphane Cordier Université d'Orléans 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 Autònoma de Barcelona June 28 July 17
Nicolas Dirr University of Bath July 18 July 25
Jean Dolbeault Université Paris Dauphine June 21 July 17
Italo Capuzzo Dolcetta Università Roma La Sapienza July 18 July 24
Pierpaolo Esposito Università 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
Mi-Ho Giga University of Tokyo July 22 August 7
Changfeng Gui University of Connecticut July 1 August 1
Cyril Imbert Université Paris-Dauphine 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 Jyväskylä 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 Université d'Orléans June 28 July 5
Juan Jose Manfredi University of Pittsburgh July 26 August 1
Florian Mehats Université de Rennes 1 June 21 July 9
Luc Mieussens Université 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 Müller 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 Université 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 Rivière Swiss Federal Institute of Technology (ETH) July 4 July 24
Frederic Robert Université de Nice Sophia-Antipolis July 5 July 21
Russell Schwab University of Texas at Austin July 18 July 25
Eric Séré Univerisité 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 Université Paul Cézanne 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 Köln 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