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

Scientific Committee:

  • Gui-Qiang Chen, University of Oxford
  • Marshall Slemrod, University of Wisconsin
  • László Székelyhidi, Leipzig University

Local Organising Committee:

  • Heiko Gimperlein, Heriot-Watt University
  • Robin Knops, Heriot-Watt University
  • Beatrice Pelloni, Heriot-Watt University
 
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)
  • Tristan Buckmaster, Princeton University
  • Martina Hofmanova, Bielefeld University
  • Elisabetta Chiodaroli, University of Pisa
  • Diego Cordoba, Instituto de Ciencias Matematicas, Madrid
  • Daniel Faraco, Universidad Autonoma de Madrid, Madrid
  • Eduard Feireisl, Czech Academy of Sciences
  • Dominik Inauen, Leipzig
  • Philip Isett, University of Texas
  • Filip Rindler, University of Warwick
  • Angkana Rueland, Max Planck Institute, Leipzig
  • Edriss Titi, University of Cambridge and University of Texas A and M
  • Vlad Vicol, Courant Institute, New York
  • Barbara Zwicknagl, Humboldt University, Berlin

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

Arrangements

Registration has now closed. Further information on final arrangements will be sent to all in-person and online participants nearer the time.

Programme

Monday 8 November
12.00-13.15 Lunch and Registration
13.15-13.20 Welcome and Opening Remarks
13.20-14.05 Diego Cordoba (live ICMS)
14.05-14.50 Angkana Ruland (zoom)
14.50-15.00 Break
15.00-17.00 Camillo De Lellis - Clay course (zoom) - slides are available here
17.10-17.55 Philip Isett (zoom) - slides are available here
17.55-19.00 Light Supper and refreshments

Tuesday 9 November
12.00-13.00 Lunch
13.15-14.00 Filip Rindler (zoom) - slides are available here
14.00-14.45 Tristan Buckmaster (zoom)
14.45-15.00 Break
15.00-17.00 Camillo De Lellis - Clay course (zoom) - slides are available here
17.00-17.30 Break
17.30-18.30 Vincent Borrelli - Public Lecture (live ICMS)
18.30-19.30 Light Supper and refreshments

Wednesday 10 November
12.00-13.00 Lunch
13.00-13.25 Luigi De Rosa (zoom)
13.25-13.50 Tomasz Debiec (zoom)
13.50-14.15 Jozsef Kolumban (zoom)
14.15-14.40 Bjorn Gebhard (live ICMS) - slides are available here
14.40-15.00 Break
15.00-15.45 Daniel Faraco (zoom)
15.45-16.30 Elisabetta Chiodaroli (zoom)
16.30-17.15 Edriss Titi (zoom)
17.15-17.30 Break
17.30-18.15 Vlad Vicol (zoom)
18.15-19.15 Light Supper and refreshments

Thursday 11 November
12.00-13.00 Lunch
13.00-13.25 Informal Discussion
13.25-13.50 Stefano Modena (zoom)
13.50-14.15 Gabriel Sattig (zoom) - slides are available here
14.15-14.40 Jan Burczak (zoom) - slides are available here
14.40-15.00 Break
15.00-15.45 Barbara Zwicknagl (zoom)
15.45-16.30 Dominik Inauen (live ICMS)
16.30-17.15 Martina Hofmanova (zoom) - slides are available here
17.15-18.15 Light Supper and refreshments

Friday 12 November
12.00-13.00 Lunch
13.00-13.25 Informal Discussion
13.25-13.50 Paolo Bonicatto (zoom) - slides are available here
13.50-14.15 Koji Ohkitani (zoom) - slides are available here
14.15-14.35 Break
14.35-15.10 Eduard Feireisl (zoom) - slides are available here
15.10-15.15 Closing Remarks


Recordings of talks can be viewed here

Speakers, talk titles and abstracts can be viewed here

For any queries, please contact Simon Kershaw at ICMS (simon.kershaw at icms.org.uk)