# Geometric Analysis, Elasticity and PDE

*23 - 27 Jun 2008*

*Heriot Watt University*

#### Scientific Organisers:

**Jerry Bona**, University of Illinois**Jack Carr**, Heriot-Watt University**Richard James**, University of Minnesota**Jerry Marsden**, California Institute of Technology**François Murat**, Université Pierre et Marie Curie**Marshall Slemrod**, University of Wisconsin

#### Local Organising Committee:

**Tony Carbery**, University of Edinburgh**Jack Carr,**Heriot-Watt University**Chris Eilbeck**, Heriot-Watt University**Robin Knops**, Heriot-Watt University**John Toland**, University of Bath

2008 sees the 60th birthday of Sir John Ball, FRS, FRSE and we celebrated this occasion during the workshop. Lecture notes and photographs are available here.

#### Objectives:

Mapping new frontiers of research

Building bridges between the most recent developments in the general mathematical theory and the areas of applications that have developed most actively in the last few years,

Identifying new applications of PDE

#### Themes:

Nonlinear elasticity and liquid crystals

Material science; microstructure, minimizer in the presence of symmetry, relation with experiment

Calculus of variations

Systems of conservation laws

Transport equations

Biomaterials Dynamical systems methods and the PDEs of mechanics

#### Speakers:

**Vladimir Sverak,**University of Minnesota*- Liouville Theorems for the Navier-Stokes Equations***Maria J. Esteban,**CEREMADE*- Critical Magnetic Field for the Dirac-Coulomb Model***Carme Calderer**, University of Minnesota*- Nonlinear Elasticity and Liquid Crystals in Biological and Biomedical Application***Stuart Antman**, University of Maryland*- Asymptotics of Small Inertias and Large Times in Nonlinear Continuum Mechanics***Constantine Dafermos,**Brown University*- Elastodynamics and John Ball***Robert Pego,**Carnegie Mellon University*- How to Compute the Pressure in Incompressible Viscous Flow with No-Slip Boundary***Terry Tao,**University of California*- Global Regularity of Wave Maps via Harmonic Map Heat Flow***Yann Brenier,**Université de Nice-Sophia-Antipolis*- Convection, Magnetic Relaxation and Optimal Transport***Carsten Carstensen,**Humboldt-Universität*- Computational Challenges in the Calculus of Variations***Antonio DeSimone,**SISSA*- Excellent Swimmers***Oliver Penrose,**Heriot-Watt University*- Statisical Mechanics of Nonlinear Elasticity in the System of Hard Disks***Gero Friesecke,**University of Warwick*- A Mathematical Picture of Basic Aspects of the Periodic Table***Bob Kohn**, New York University*- Cloaking by Change of Variables***Stefan Müller**, Max Planck Institute for Mathematics*- Some Thoughts about Crystals and the Cauchy-Born Rule at Positive Temperature***Sergio Conti**, Universität Bonn*- Patterns in Thin Elastic Sheets***Philippe Ciarlet**, City University of Hong Kong*- Intrinsic Elasticity***Nick Schryvers**, University of Antwerp*- Nano- and Microstructures Charaterized by Transmission Electron Microscopy***Kaushik Bhattacharya,**California Institute of Technology*- Electronic Structure and Macroscopic Properties of Solids*

**This workshop was supported by the EPSRC, the Maxwell Institute for Mathematical Sciences, the University of Oxford, the LMS and the Edinburgh Mathematical Society.**

### Participants

Name | Institution |
---|---|

Stefan, Adams | University of Warwick |

Stuart, Antman | University of Maryland |

John, Ball | Heriot-Watt University |

Peter, Bates | Michigan State University |

Margaret, Beck | Heriot-Watt University |

Kaushik, Bhattacharya | California Institute of Technology |

Natalia, Bochkina | University of Edinburgh |

David, Bourne | University of Glasgow |

Yann, Brenier | Ecole Polytechnique |

Ken, Brown | Heriot-Watt University |

Martin, Burns | University of Strathclyde |

Carme, Calderer | University of Minnesota |

Yves, Capdeboscq | University of Oxford |

Anthony, Carbery | University of Edinburgh |

Jack, Carr | Heriot-Watt University |

Carsten, Carstensen | Humboldt-Universität zu Berlin |

Isaac, Chenchiah | University of Bristol |

Kirill, Cherednichenko | University of Bath |

Miroslav, Chlebik | University of Sussex |

Adam, Chmaj | Warsaw University of Technology |

Philippe G., Ciarlet | City University of Hong Kong |

Sergio, Conti | Universität Bonn |

Daniel, Coutand | Heriot-Watt University |

Elaine, Crooks | University of Swansea |

Bernard, Dacorogna | École Polytechnique Fédérale de Lausanne |

Constantine, Dafermos | Brown University |

Fordyce, Davidson | University of Dundee |

Penny, Davies | University of Strathclyde |

Antonio, DeSimone | Scuola Internazionale Superiore di Studi Avanzati |

Wlodzimierz, Domanski | Polish Academy of Sciences |

Patrick, Dondl | Durham University |

Robert, Douglas | Aberystwyth University |

Dugald, Duncan | Heriot-Watt University |

Angel, Duran | University of Valladolid |

J. Chris, Eilbeck | Heriot-Watt University |

Maria J, Esteban | Université Paris-Dauphine |

Jozsef, Farkas | University of Stirling |

Gilles A., Francfort | Université Paris-Nord |

Gero, Friesecke | TU Munich |

Michael, Grinfeld | University of Strathclyde |

Mark, Haskins | Imperial College London |

Duvan, Henao | University of Oxford |

Viet Ha, Hoang | Nanyang Technological University |

Gunnar, Hornig | University of Dundee |

Peter, Hornung | University of Bath |

Cheng-Hsiung, Hsu | National Central University,Taiwan |

Wen-Guei, Hu | National Chiao Tung University |

Richard, James | University of Minnesota |

Abdelouahab, Kadem | University of Setif |

Agnieszka, Kalamajska | University of Warsaw |

Biswajit, Karmakar | Max Planck Institute |

Abdul Rahim, Khan | King Fahd University of Petroleum and Minerals |

Robin, Knops | Heriot-Watt University |

Gabriel, Koch | University of Chicago |

Robert V., Kohn | New York University |

Gerasim, Kokarev | University of Leeds |

Michalis, Kontovourkis | Max Planck Institute |

Konstantinos, Koumatos | University of Oxford |

Jan, Kristensen | University of Oxford |

Andrew, Lacey | Heriot-Watt University |

Ben, Leimkuhler | University of Edinburgh |

Gabriel, Lord | Heriot-Watt University |

Alex, Mahalov | Arizona State University |

Emmanuel, Maitre | Université de Grenoble |

Maroje, Marohnic | University of Zagreb |

Karsten, Matthies | University of Bath |

Christof, Melcher | University of Oxford |

Roger, Moser | University of Bath |

Benson, Muite | University of Oxford |

Stefan, Müller | Max Planck Institute |

François, Murat | Université Pierre et Marie Curie (Paris VI) |

Camil, Muscalu | Cornell University |

Sergiy, Nesenenko | Darmstadt University of Technology |

Stefan, Neukamm | TU München |

Igor, Neygebauer | National University of Rwanda |

Barbara, Niethammer | University of Bonn |

Michael, Ortiz | California Institute of Technology |

Christoph, Ortner | University of Warwick |

Felix, Otto | Max Planck Institute for Mathematics in the Sciences, Leipzig |

Iryna, Pankratova | Narvik University College |

Robert, Pego | Carnegie Mellon University |

Oliver, Penrose | Heriot-Watt University |

Mircea, Petrache | Scuola Normale Superiore |

Andrey, Piatnitski | Narvik University College |

Andrey, Rekalo | Heriot-Watt University |

David, Rule | University of Edinburgh |

Bryan, Rynne | Heriot-Watt University |

Witold, Sadowski | University of Warwick |

Dominique (Nick), Schryvers | University of Antwerp |

Yasemin, Sengul | University of Oxford |

Gregory, Seregin | University of Oxford |

Hélia, Serrano | Universidad de Castilla-La Mancha |

Eugene, Shargorodsky | King's College London |

Michael, Shearer | North Carolina State University |

Michael, Singer | University College London |

Jeyabal, Sivaloganathan | University of Bath |

Valeriy, Slastikov | University of Bristol |

Marshall, Slemrod | University of Wisconsin |

Wolfgang, Staubach | Heriot-Watt University |

Philipp Emanuel, Stelzig | TU München/Università di Trento |

Pawel, Strzelecki | University of Warsaw |

Endre, Suli | University of Oxford |

Vladimir, Sverak | University of Minnesota |

László, Székelyhidi | Leipzig University |

Ali, Taheri | University of Sussex |

Josip, Tambaca | University of Zagreb |

Antoine, Tambue | Heriot-Watt University |

Terence, Tao | University of California at Los Angeles |

John, Toland | Isaac Newton Institute for Mathematical Sciences |

Basang, Tsering | University of Oxford |

Igor, Velcic | University of Zagreb |

David, Wagner | University of Houston |

Stephen, Watson | University of Glasgow |

Tzi-Sheng, Yang | Tunghai University |

Ting-Hui, Yang | Tamkang University |

Arghir, Zarnescu | University of Sussex |

Kewei, Zhang | University of Swansea |