Regularity Theory for Free Boundary and Geometric Variational Problems III

Levico Terme, 19-23 June 2023


ERC VaReg (European Union - Horizon 2020)

Centro Internazionale di Ricerca Matematica - Fondazione Bruno Kessler


        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.



Tristan Rivière (ETH Zürich)

Susanna Terracini (Università di Torino)

Francesco Maggi (UT Austin)

Donatella Danielli (Arizona State University)

Yannick Sire (Johns Hopkins University)

Guido De Philippis (Courant Institute - NYU)

Gianmaria Verzini (Politecnico di Milano)

Costante Bellettini (University College London)

Zihui Zhao (Johns Hopkins University)

Robin Neumayer (Carnegie Mellon University)

Mariana Smit Vega Garcia (Western Washington University)

Antonio De Rosa (University of Maryland)

Jonas Hirsch (Universität Leipzig)

Hui Yu (National University of Singapore)

Nick Edelen (University of Notre Dame)

Max Engelstein (University of Minnesota)

Simone Steinbrüchel (Universität Leipzig)

Salvatore Stuvard (Università di Milano)

Annalisa Massaccesi (Università di Padova)

Antoine Song (California Institute of Technology)

Christos Mantoulidis (Rice University)

Andrea Marchese (Università di Trento)

Xavier Fernández-Real (EPFL - Lausanne)

Dario Mazzoleni (Università di Pavia)

Stefano Vita (Università di Torino)

Alessandro Audrito (Politecnico di Torino)

Anna Skorobogatova (Princeton University)

Alessandro Pigati (Bocconi)

Riccardo Tione (MPI Leipzig)

Nicola Garofalo (Università di Padova)

Federico Franceschini (ETH Zürich)

Paul Minter (Princeton)

Ian Flescher (Princeton)

Marco Badran (Univesity of Bath)

Emanuele Salato (Università di Torino)

Gabriele Fioravanti (Università di Torino)

Kobe Marshall Stevens (University College London)

Lorenzo Sarnataro (Princeton)

Alexis Michelat (EPFL)

Alessandra Pluda (Università di Pisa)

Luigi De Masi (Università di Padova)

Matteo Carducci (Scuola Nuormale Superiore)

Luca Benatti (Università di Pisa)

Lorenzo Ferreri (Scuola Nuormale Superiore)

Giulia Bevilacqua (Università di Pisa)

Davide Parise (University of California San Diego)

Carlo Gasparetto (Università di Pisa)

Giorgio Tortone (Università di Pisa)

Roberto Ognibene (Università di Pisa)

Luca Spolaor (University of California San Diego)

Bozhidar Velichkov (Università di Pisa)


Monday 19 June

09:00-09:50   Susanna Terracini

Boundary Harnack principles and degenerate equations on singular sets

10:10-11:00   Hui Yu

Compact contact sets in the thin obstacle problem

11:40-12:30   Andrea Marchese

On the closability of differential operators

15:00-15:50   Giorgio Tortone

On the regularity of the optimal shapes for a class of integral functionals

16:10-17:00   Mariana Smit Vega Garcia

Almost minimizers of a lower-dimensional free boundary problem

Tuesday 20 June

09:00-09:50   Tristan Rivière

Area variations under lagrangian and legendrian constraints

10:10-11:00   Costante Bellettini

Hypersurfaces with mean curvature prescribed by an ambient function

11:40-12:30   Salvatore Stuvard

Existence and regularity of Brakke flows: new advances and open questions

15:00-15:50   Anna Skorobogatova

Higher codimension area-minimizers: rectifiability of singularities and Hm-2-a.e. uniqueness of tangent cones

16:10-17:00   Alessandro Pigati

Nondegenerate minimal submanifolds as energy concentration sets

Wednesday 21 June

09:00-09:50   Donatella Danielli

Obstacle problems for fractional powers of the Laplacian

10:10-11:00   Max Engelstein

On global graphical solutions to free boundary problems

11:40-12:30   Gianmaria Verzini

Stationary and rotating spirals in segregated reaction-diffusion systems

Thursday 22 June

09:00-09:50   Jonas Hirsch

Interior regularity for two-dimensional stationary Q-valued maps

10:10-11:00   Christos Mantoulidis

Generic regularity of minimizing hypersurfaces in dimensions 9 and 10

11:40-12:30   Antoine Song

Hyperbolic groups and spherical minimal varieties

15:00-15:50   Robin Neumayer

Local minimizers of the anisotropic isoperimetric problem on closed manifolds

16:10-17:00   Riccardo Tione

Non-Classical solutions to the p-Laplace equation

Friday 23 June

09:00-09:50   Francesco Maggi


10:10-11:00   Zihui Zhao

Counter-example in boundary unique continuations

11:40-12:30   Yannick Sire

Geometric structure for nodal sets of solutions to degenerate and singular equations


Book of abstracts

Organizers: Luca Spolaor and Bozhidar Velichkov

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