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 the formation and the structure of singularities.
Participants
Yannick Sire (Johns Hopkins University)
Henrik Shahgholian (KTH Stockholm)
Leon Simon (Stanford University)
Guy David (Université de Paris Sud)
Jonas Hirsch (Universität Leipzig)
Francesco Maggi (University of Texas)
Guido De Philippis (Courant Institute)
Felix Schulze (University of Warwick)
Nick Edelen (Notre Dame University)
Matteo Focardi (Università di Firenze)
Hui Yu (National University of Singapore)
Mariana Smit Vega Garcia (Western Washington University)
Nicola Soave (Politecnico di Milano)
Stefano Vita (Università di Torino)
Dario Mazzoleni (Università di Pavia)
Xavier Fernández-Real (EPFL - Lausanne)
Salvatore Stuvard (Università di Milano)
Antonio De Rosa (University of Maryland)
Andrea Marchese (Università di Trento)
Alessandra Pluda (Università di Pisa)
Anna Skorobogatova (Princeton University)
Mickael Nahon (Université de Savoie)
Simone Steinbrüchel (Universität Leipzig)
Riccardo Tione (MPI Leipzig)
Davide Parise (Cambridge)
Federico Franceschini (ETH Zürich)
Carlo Gasparetto (SISSA Trieste)
Paul Minter (Cambridge)
Giulia Bevilacqua (Politecnico di Torino)
Giorgio Tortone (Università di Pisa)
Roberto Ognibene (Università di Pisa)
Luca Spolaor (University of California San Diego)
Bozhidar Velichkov (Università di Pisa)
Schedule
Monday 11 July
(Aula Magna - Polo Fibonacci)
09:00-09:50 Leon Simon
Construction of singular minimal hypersurfaces
10:10-11:00 Francesco Maggi
A mesoscale flatness criterion and its application to exterior isoperimetry
11:40-12:30 Guido De Philippis
Non-degenerate minimal surfaces as energy concentration sets: a variational approach
15:00-15:50 Anna Skorobogatova
Higher codimension area-minimizers: understanding interior branch points via the frequency function
16:10-17:00 Carlo Gasparetto
Regularity for the mean curvature flow with boundary
Tuesday 12 July
(Aula Magna - Dipartimento di Matematica)
09:00-09:50 Henrik Shahgholian
A free boundary perspective on transmission and inverse scattering problems
10:10-11:00 Guy David
Regularity (quantitative convexity) of the boundary for subsets of a convex domain that almost minimize the perimeter
11:40-12:30 Hui Yu
Contact points with integer and 7/2 frequencies in the thin obstacle problem
15:00-15:50 Simone Steinbrüchel
Generic uniqueness for optimal transportation networks
16:10-17:00 Federico Franceschini
Free boundary partial regularity in the thin obstacle problem
Wednesday 13 July
(Aula Magna - Dipartimento di Matematica)
09:00-09:50 Felix Schulze
Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
10:10-11:00 Alessandra Pluda
Network flow: resolution of singularities and stability
11:40-12:30 Salvatore Stuvard
Area minimizing hypersurfaces modulo p: regularity and structure of singular sets
Thursday 14 July
(Aula Magna - Dipartimento di Matematica)
09:00-09:50 Nick Edelen
A strong maximum principle for minimizers of the one-phase Bernoulli problem
10:10-11:00 Riccardo Tione
The multi-bubble problems for convex sets
11:40-12:30 Jonas Hirsch
On the De Giorgi-Nash-Moser theorem for hypoelliptic operators
15:00-15:50 Mickaël Nahon
Free discontinuity problems in Stokes fluids
16:10-17:00 Paul Minter
Branched regularity theorems for stable codimension one stationary integral varifolds near higher multiplicity cones
Friday 15 July
(Aula Magna - Polo Fibonacci)
09:00-09:50 Xavier Fernández-Real
Optimal regularity for the fully nonlinear thin obstacle problem
10:10-11:00 Antonio De Rosa
Min-max construction of anisotropic CMC surfaces
11:40-12:30 Mariana Smit Vega Garcia
Branch points for (almost-)minimizers of two-phase free boundary problems
