Regularity Theory for Free Boundary and Geometric Variational Problems II

Pisa, 10-15 July 2022


ERC VaReg (European Union - Horizon 2020)


     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. 


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)


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


Book of abstracts

Scientific organizers: Luca Spolaor and Bozhidar Velichkov

Organizers: Luca Spolaor (UCSD), Francesca Menconi and Bozhidar Velichkov (University of Pisa)

Contacts: bozhidar.velichkov[at], lspolaor[at], francesca.menconi[at]