Research Programs


Geometric aspects of nonlinear partial differential equations

29 August - 09 December 2022

A large amount of problems in applied sciences can be described and modelled by nonlinear PDEs. Although modeling has been the most important element for the field to grow in the past, we have seen a tremendous amount of theoretical development of independent interest of the field of nonlinear PDEs. Another momentum of this surge of development comes from the fact that understanding theoretical aspects of the field, has given better understanding of several real-world phenomena and industrial processes, as well as various modeling problems within diverse areas of applications.

Topics consider in the program include:

  • Fully nonlinear PDEs (equations from differential geometry including the Monge Ampere equation)
  • Regularity of free boundaries (epiperimetric inequalities and geometric measure theory techniques)
  • Optimal transportation problems (in e.g. shape optimization and statistical mechanics)
  • Geometric flows (Ricci flow and mean curvature flow)
  • Functional inequalities (quantitive description of extremal and sharp inequalities)
  • Segregation/ interaction of species (reaction-diffusion systems and separation of phases)


During the program, there will be two workshops:

  • Introductory September 5 - 9
  • October 31 - November 4
Panagiota Daskalopoulos
Columbia University
Alessio Figalli
ETH Zürich
Erik Lindgren
Uppsala University
Henrik Shahgholian
KTH Royal Institute of Technology
Susanna Terracini
University of Turin


Erik Lindgren

Henrik Shahgholian


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