March  1, 2024

Thematic Program on Partial Differential Equations
August 2003 - June 2004

Organizing Committee:
   W. Craig (McMaster)
   N. Ercolani (Arizona)
   C. Sulem (Toronto)

Scientific Committee:
   L. Bronsard (McMaster)
   W. Craig (McMaster)
   N. Ercolani (Arizona)
   R. McCann (Toronto)

   M. Sigal (Toronto)
   C. Sulem (Toronto)
   J. Toth (McGill )
   C. E. Wayne (Boston)

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Overview of the Program:

The thematic program on PDE will be focused principally on problems that stem from questions in applied mathematics and in mathematical physics. The particular choice of subject matter is dictated by a choice of active topics of research that are of particular current interest, and the mathematical taste of the Scientific Committee. As mentioned in the introduction, we are planning the fall semester of the program to be focused on elliptic and parabolic systems of partial differential equations arising in mathematical theories of super-conductivity and of phase transition phenomena in the physics of materials. The winter semester will be focused on Hamiltonian PDE, in particular hyperbolic equations and nonlinear dispersive evolution equations that arise in mathematical physics and in continuum mechanics, and on the equations of kinetic theory that arise in the study of statistical mechanics and of wave turbulence. Specific activities that we are planning for the year long thematic program include:

  • six one-week long focused scientific workshops on aspects of PDE,
  • one one-week long conference on the mathematical theory of surface water waves, to take place during the summer 2004,
  • three mini-courses, featuring several short courses on current topics,
  • at least two weekend mini-symposia focused on special topics of current interest, presented by internationally known mathematicians who are leaders in their field, taking place during the academic year,
  • two Coxeter Lecture series and one Distinguished Lecture series during the year,
  • several ongoing research seminar series that meet regularly during the academic year,
  • a series of advanced graduate courses on special topics in the field that will serve to introduce graduate students and other mathematicians to research-level results and techniques.

Detailed plans for the thematic program:

The following represents a short sketch of the activities that we are planning for the thematic program year. The details may change according to the plans of individuals to take part in the program, the precise dates of their residence at the Fields Institute, and for other reasons. The names of individuals who have confirmed participation are marked with an asterisk.

2003 Summer- Fall Semester Program:

Focus will be on elliptic and parabolic systems; pattern formation, phase transition, and superconductivity

Courses - Fall Term 2003

(associated activity) August 22, 2003
Workshop on Resonances in Linear and Nonlinear Schrodinger Equations
Invited Speakers: S. Cuccagna (Virginia), E. Kirr (Chicago) A. Tovbis (Central Florida) , M. Weinstein (Bell Laboratories)
Organizer: D. Pelinovsky (McMaster University, Canada)

August 25 - 29, 2003
Workshop on Calculus of Variations: Geometric Problems, Superconductivity, and Material Microstructures

Organizing Committee: S. Alama, L. Bronsard, R. Choksi, R. Jerrard (Co-chair), R. McCann (Co-Chair)

September 8 - June 28, 2004 (weekly)
Fields Colloquium in Applied Mathematics
Organizers: W. Craig, C. Sulem

September 10 - June, 2004 (weekly)
Fields Institute Seminar
Organizers: S. Raynor, J. Wright

September 22- 30, 2003
Short Course on Mathematical Aspects of Fluid Dynamics
Instructors: W. Craig, C. Dafermos, B. Khesin, M. Vishik

October 1 - 4, 2003
Symposium on Inverse Problems
Organizer: A. Nachman (Toronto)
Speakers: C. Croke (Pennsylvania), V. Isakov (Wichita State), H. Isozaki (Tokyo Metropolitan), S. Kurylev (Loughborough), G. Uhlmann (Washington)

October 20-22, 2003
Coxeter Lecture Series
: L. Craig Evans (Berkeley)

October 28-30, 2003
McMaster University Britton Lectures, H. Brezis (Paris VI & Rutgers)
to be held at McMaster University

November 14-18, 2003
Workshop on Patterns in Physics

Organizing Committee: R. Almgren, N. Ercolani (Chair), D. Henderson, J. Lega, M. Pugh

November 27, 2003
Fields Mini Symposium in Applied Mathematics
Speaker: Houde Han, Tsinghua University
1:30 p.m - The artificial boundary condition method for numerical solutions of PDEs on unbounded domains

(associated activity) December 11-13, 2003
Workshop on Bifurcation Theory and Spatio-Temporal Pattern Formation in PDE
in Honour of Professor William Langford
Organizers: A. Lawniczak, W. Nagata, V. LeBlanc, N. Namachchivaya

2004 Winter - Spring Semester Program:

Focus will be on Hamiltonian PDE, and on kinetic theory and turbulence.

The winter program will have four focused workshops, as well as a series of regular research seminar presentations. The first and second workshops on March 2004 and the third and fourth workshops, planned for May 2004, will be back-to-back, to take advantage of the presence of a community of mathematicians who have a research interest in both topics. In addition the 2004 mini courses will take place closely in time to these events, for the same reason that the principal speakers/instructors for the summer school courses are involved with activities closely linked to the two workshops.

Courses - Winter Term 2004

Activities Winter - Spring Program

January 31-February 1, 2004
Young Mathematicians Conference in PDE and Dynamical Systems
Organizers: Stefanella Boatto, Walter Craig, Catherine Sulem

February 4-25, 2004 (Wednesdays, 4:00 p.m.)
Short Course in Isoperimetric Inequalities for Eigenvalues of the Laplacian

Instructor: Rafael Benguria (Pontificia Universidad Católica de Chile & The Fields Institute)

March 15-19, 2004
Workshop on Nonlinear Wave Equations

Organizing Committee: C. Bardos, J. Colliander, W. Craig (Chair), N. Ercolani, C. Sulem

March 24-26, 2004
Short Course in Kinetic Theory
Organizing Committee: D. Levermore, Th. Passot, C. Sulem (Chair), P.-L. Sulem
Y. Elskens, F. Golse, D. Levermore, Th. Passot, H. Qin, P.-L. Sulem, W.M. Tang

March 29-April 2, 2004
Workshop on Kinetic Theory

Organizing Committee: D. Levermore, Th. Passot, C. Sulem (Chair), P.-L. Sulem

April 6-May 11, 2004 (weekly)
Fields Colloquium in Geometric Analysis
W. Craig, P. Guan
Speakers: Louis Nirenberg (CIMS),Guofang Wang (Max-Planck-Institut für Informatik),Rick Schoen (Stanford), Jon Wolfson (Stanford & MSU), Luis Caffarelli (University of Texas at Austin)

May 3-5, 2004
Coxeter Lecture Series

Speaker: Sergei Kuksin (Heriot-Watt)

May 10-13, 2004
Distinguished Lecture Series
Speaker: Jean Bourgain (I.A.S., Princeton & Illinois, Urbana-Champaign)

May 11-15, 2004
Short Course on Hamiltonian Partial Differential Equations
Organizers: W. Craig, S. Kuksin

May 17-21, 2004
Workshop on Integrable and Near-integrable Hamiltonian PDE
(joint with the CRM)
Organizing Committee:
W. Craig (Chair), P. Deift, S. Kuksin, P. Olver, J. Toth, P. Winternitz

May 24-28, 2004
Workshop on Hamiltonian Dynamical systems
(at CRM, Montreal)
Organizing Committee: D. Bambusi, W. Craig, S. Kuksin, C.E. Wayne (Chair), E. Zehnder

June 1-11, 2004
Workshop on Semi-classical Theory of Eigenfunctions and PDEs (joint with CRM)
Organizers: D. Jakobson, J. Toth
       June 1-5, Workshop will be held at Centre de recherches mathématiques (CRM), Montreal
       June 7-11 , Workshop will be held at The Fields Institute, Toronto

June 14-18, 2004
Workshop on Free Surface Water Waves

Organizing Committee:
J. Carter, W. Craig, B. Deconinck, J. Hammack, D. Henderson, D. Nicholls, H. Segur, C. Sulem

Research seminars:

We expect to run several research seminars during the year, meeting weekly on a regular basis, and involving the postdoctoral fellows and graduate students who are associated with the program. The seminar series will be coordinated with the CRM in Montréal, during their coincident year long program on Analysis.

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