Description
This workshop is dedicated to the recent advances in the theories of
Free Boundary Problems and Minimal Surfaces
which include problems and combine tools from different fields as for instance
PDEs, Calculus of Variations and Geometric Analysis.
The main topic is the regularity and the fine structure of geometric objects
(free boundaries, minimal surfaces, free interfaces)
obtained trough the minimization of variational functionals. The description of the local structure of these minima is a common objective
for both the fields of Free Boundary Problems and Minimal Surfaces and the techniques developed in this context have found application
to problems from different areas.
The workshop brings together young researchers and leading experts in these fields, the focus being on
the recent important breakthroughs in the regularity of the free boundaries
and minimal surfaces, in particular, on questions related to the formation and the structure of singularities.
Participants
Alessandro Audrito (ETH Zürich)
Dorin Bucur (Université de Savoie)
Joseph Feneuil (Università di Pisa)
Xavier Fernandez-Real (EPFL - Lausanne)
Alessio Figalli* (ETH Zürich)
Matteo Focardi (Università di Firenze)
Nicolò Forcillo (Unversità di Bologna)
Serena Guarino Lo Bianco* (University of Naples)
Jonas Hirsch (Universität Leipzig)
Domenico Angelo La Manna (University of Jyväskylä)
Francesco Paolo Maiale (Scuola Normale Superiore)
Andrea Marchese (Università di Trento)
Annalisa Massaccesi (Università di Padova)
Dario Mazzoleni (Università di Pavia)
Andrea Mondino* (University of Oxford)
Connor Mooney (UC Irvine)
Ekaterina Mukoseeva (University of Helsinki)
Mickael Nahon (Université de Savoie)
Robin Neumayer (Carnegie Mellon)
Xavier Ros-Oton* (Universitat de Barcelona)
Yannick Sire (Johns Hopkins University)
Nicola Soave (Politecnico di Milano)
Luca Spolaor (University of California San Diego)
Simone Steinbrüchel* (Universität Leipzig)
Susanna Terracini (Università di Torino)
Riccardo Tione (EPFL - Lausanne)
Giorgio Tortone (Università di Pisa)
Bozhidar Velichkov (Università di Pisa)
Stefano Vita (Università di Milano-Bicocca)
Neshan Wickramasekera* (University of Cambridge)
Zihui Zhao (University of Chicago)
* = remote participation
Schedule
Monday 6 Sept
09:00-09:50 Susanna Terracini
Free boundaries in segregation problems
10:10-11:00 Andrea Marchese
Area minimizing currents mod p: general regularity theory
11:40-12:30 Connor Mooney
The Bernstein problem for equations of minimal surface type
15:00-15:50 Alessandro Audrito
Interface regularity and 1D symmetry for semilinear one-phase problem
16:10-17:00 Giorgio Tortone
The capillarity one-phase problem
Tuesday 7 Sept
09:00-09:50 Andrea Mondino
Optimal transport, weak Laplacian bounds and minimal boundaries
in non-smooth spaces with lower Ricci curvature bounds
10:10-11:00 Alessio Figalli
Generic regularity in obstacle problems
11:40-12:30 Domenico Angelo La Manna
Charged liquid drop
15:00-15:50 Stefano Vita
Strong unique continuation and local asymptotics
at the boundary for fractional elliptic equations
16:10-17:00 Nicolò Forcillo
A perturbative estimates approach to the free boundary regularity
in the one-phase Stefan problem
Wednesday 8 Sept
09:00-09:50 Xavier Ros-Oton
Stable cones in the thin one-phase free boundary problem
10:10-11:00 Jonas Hirsch
Area minimizing hypersurfaces mod(p): A geometric free boundary problem
11:40-12:30 Annalisa Massaccesi
Frobenius theorem for weak submanifolds
Thursday 9 Sept
09:00-09:50 Dorin Bucur
Multiphase free discontinuity problems: monotonicity formula and regularity results
10:10-11:00 Dario Mazzoleni
A spectral shape optimization problem with a nonlocal competing term
11:40-12:30 Robin Neumayer
Quantitative Faber-Krahn inequalities and the ACF Monotonicity Formula
15:00-15:50 Yannick Sire
Some results on harmonic maps with free boundary and beyond
16:10-17:00 Simone Steinbrüchel
Boundary regularity for higher multiplicity boundaries of 2D area minimizing currents
Friday 10 Sept
09:00-09:50 Nicola Soave
Free boundary problems in the spatial segregation of some competing systems
10:10-11:00 Zihui Zhao
Boundary unique continuation of Dini domains
11:40-12:30 Matteo Focardi
On the regularity of singular sets of minimizers for the Mumford-Shah energy
