Convex Integration and Nonlinear Partial Differential Equations

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Convex Integration and Nonlinear Partial Differential Equations

 08 - 12 Nov 2021
 ICMS, Bayes Centre, 47 Potterrow Edinburgh

Organisers:

  • Gui-Qiang Chen, University of Oxford
  • Heiko Gimperlein, Heriot-Watt University
  • Robin Knops, Heriot-Watt University
  • Beatrice Pelloni, Heriot-Watt University
  • Marshall Slemrod, University of Wisconsin
  • László Székelyhidi, Leipzig University
 
Update May 2021: We are making plans for a hybrid workshop, provided that regulations are sufficiently relaxed to allow us to do this, but we do have a plan to move to an entirely online workshop, if necessary, with all participants joining remotely.
 
Significant advances in the field of convex integration will be explained and discussed by leading specialists involved in the subject's resurgence. Convex integration originated with the Nash-Kuiper (1954/55) isometric embedding theorem and is central to Gromov's h-principle (1986). The highly irregular (wrinkled) solutions which are a prominent feature have recently found application in other important contexts. Long standing conjectures such as that by Onsager on turbulence have been successfully resolved. Connexions have been established with several nonlinear partial differential equations including those for fluid and solid continuum mechanics. Numerical simulation of solutions has enhanced intuition and illustrated geometrical and physical properties. Challenging open problems remain, however and offer a rich potential for future research. These topics form the main themes of the Workshop.

The workshop, which will include of an expository course by Clay lecturer De Lellis, to supplement the research presentations, is open to all and especially those from the UK and international communities who wish to either acquire or expand knowledge of this intriguing theory and its striking applications.

Invited Speakers:

  • Vincent Borelli, University of Lyon, (Public Lecture)
  • Camillo De Lellis, IAS Princeton (Clay Lecturer, expository course)
  • Luca Biferale, University of Rome Vergata
  • Elisabetta Chiodaroli, University of Pisa
  • Maria Colombo, EPFL, Lausanne
  • Diego Cordoba, Instituto de Ciencias Matematicas, Madrid
  • Daniel Faraco, Universidad Autonoma de Madrid, Madrid
  • Eduard Feireisl, Czech Academy of Sciences
  • Philip Isett, University of Texas
  • Filip Rindler, University of Warwick
  • Angkana Rueland, Max Planck Institute, Leipzig
  • Roman Shvydkoy, University of Illinois, Chicago
  • Boris Thibert, University of Grenoble Alpes
  • Edriss Titi, University of Texas A and M
  • Vlad Vicol, Courant Institute, New York
  • Barbara Zwicknagl, Technical University, Berlin

This workshop is organised in partnership with the Clay Mathematics Institute.

Arrangements

Information regarding participation will be posted here shortly. This workshop has been rescheduled from July 2020.