Free Boundary Problems

Free Boundary Problems are ubiquitous in applications. Their mathematical treatment is a mainstay in applied mathematics and has inspired a large international community. This Thematic Program is designed to offer a platform for exchange and collaboration. Rhree workshops are planned, namely:

Workshop 1, Sept. 29 -Oct. 3, 2025: Regularity of free boundary problems;

Workshop 2, Nov. 10 -  Nov. 14, 2025: Geometric variational problems;

Workshop 3, Dec. 9 - Dec.12, 2025: Free boundaries and growth.

In addition, we will series of lectures and seminars, including

Jose' A. Carrillo (Oxford): Global minimizers of interaction energies, 3h, Oct. 7 (14-15:30) and Oct. 9 (10-11:30), 2025.

Yoshihiro Tonegawa (Institute of Science Tokyo): Introduction to Brakke's mean curvature flow, 12h, Oct. 27 - Nov. 5, 2025. Link to the course website

Joaquim Serra (ETH): Stable solutions to the Allen-Cahn equation with bounded energy density, 3h, Nov. 17 -  Nov. 18, 2025.

Max Fathi (Paris): Quantitative regulairty for ransport maps, 6h, Nov. 20 - Nov. 21, 2025.

Please note that participation into the Thematic Programme is by invitation only.

Partial support is acknowledged from the SFB 65 Project Taming Complexity in Partial Differential Systems, financed through a grant by the Austrian Science Fund (FWF).

 

Sept. 29, 2025
09:00 — 09:30
Registration & Welcome
10:30 — 11:00
Coffee Break
12:00 — 14:00
Lunch Break
14:00 — 15:00
Jack Thompson (UWA, Perth)
The nonlocal halfspace theorem
15:00 — 15:30
Coffee Break
15:30 — 16:30
Claudia Bucur (U degli Studi di Milano)
S-minimal functions: existence and continuity
Sept. 30, 2025
10:30 — 11:00
Coffee Break
11:00 — 12:00
Mihalis Mourgoglou (Universidad del País Vasco)
Two-Phase Problems for Elliptic Measures for DMO Elliptic Operators
12:00 — 14:00
Lunch Break
14:00 — 15:00
Xavier Fernandez-Real (EPFL, Lausanne)
Stable solutions for the one-phase problem
15:00 — 15:30
Coffee Break
15:30 — 16:30
Oct. 1, 2025
09:00 — 10:00
10:00 — 11:00
Mateusz Kwaśnicki (UST Wroclaw)
Liouville's theorems for Lévy operators
11:00 — 11:30
Coffee Break
11:30 — 12:30
Oct. 2, 2025
10:30 — 11:00
Coffee Break
12:00 — 14:00
Lunch Break
14:00 — 15:00
15:00 — 15:30
Coffee Break
15:30 — 16:30
Oct. 3, 2025
09:30 — 10:30
10:30 — 11:00
Coffee Break
Oct. 7, 2025
14:00 — 15:30
Jose‘ A. Carrillo (U Oxford)

Global minimizes of interaction energies I

Oct. 9, 2025
10:00 — 11:30
Jose’ A. Carrillo (U Oxford)

Global minimizers of interaction energies II

Oct. 10, 2025
12:00 — 12:45
Dirk Peschka (WIAS Berlin)

Thin-Film Free Boundary Problems with Moving Contact Lines - Modelling, Numerics, and Model Hierarchies

Oct. 15, 2025
12:00 — 12:45
Konstantinos Koumatos (Sussex)

On the role of quasiconvexity in dynamics

Oct. 27, 2025
15:15 — 17:00
Oct. 28, 2025 Oct. 29, 2025
15:15 — 17:00
Oct. 30, 2025
12:30 — 13:15
Robert Lasarzik (WIAS Berlin)

The energy-variational structure in evolution

Oct. 31, 2025
15:15 — 17:00
Nov. 3, 2025
15:15 — 17:00
Nov. 5, 2025
15:15 — 17:00
Nov. 10, 2025
09:00 — 09:15
Registration
09:15 — 09:55
10:35 — 11:00
Coffee break
11:00 — 11:40
11:40 — 12:20
12:20 — 14:00
Lunch break
14:00 — 14:40
15:20 — 15:45
Coffee break
15:45 — 16:15
Nov. 11, 2025
09:40 — 10:20
10:20 — 11:00
Coffee break
11:00 — 11:40
Michael Goldman (CNRS & Ecole Polytechnique, Palaiseau)
Variational models for charge liquid drops
11:40 — 12:20
12:20 — 14:00
Lunch break
14:00 — 14:40
14:40 — 15:20
15:20 — 16:00
Coffee break
16:00 — 16:40
Nov. 12, 2025
09:00 — 09:40
09:40 — 10:20
10:20 — 11:00
Coffee break
11:00 — 11:40
11:40 — 12:20
Paola Pozzi (U Duisburg-Essen)
Elastic Flow Revisited
12:20 — 13:00
Nov. 13, 2025
09:40 — 10:20
10:20 — 11:00
Coffee break
11:40 — 12:20
12:20 — 14:00
Lunch break
14:40 — 15:20
15:20 — 15:45
Coffee break
15:45 — 16:15
Enric Florit-Simon (ETH Zurich)
Regularity for stable phase transitions
Nov. 14, 2025
09:00 — 09:40
Costante Bellettini (University College London)
Bernstein-type theorems for stable minimal hypersurfaces
10:20 — 11:00
Coffee break
11:00 — 11:40
Nov. 17, 2025
14:30 — 16:00
Joaquim Serra (ETH)

Stable solutions to the Allen-Cahn equation with bounded energy density I

Nov. 18, 2025
11:30 — 13:00
Joaquim Serra (ETH)

Stable solutions to the Allen-Cahn equation with bounded energy density II

Nov. 20, 2025
14:00 — 16:30
Max Fathi (Paris)

Quantitative regularity for transport maps I

Nov. 21, 2025
14:00 — 16:30
Max Fathi (Paris)

Quantitative regularity for transport maps II

Nov. 26, 2025
14:00 — 14:45
Verena Bögelein (U of Salzburg)

Self-improvement phenomena in nonlinear evolution equations

Location: Schrödinger Lecture Hall

Nov. 28, 2025
14:00 — 14:45
Frank Duzaar (U of Salzburg)

Parabolic PDEs with Dynamic Data under a Bounded Slope Condition

Location: Schrödinger Lecture Hall

Dec. 9, 2025
09:00 — 09:15
Registration
09:15 — 09:30
Welcoming words
10:00 — 10:30
11:00 — 11:30
Coffee break
12:00 — 12:30
Pasquale Ciarletta (Politecnico Milano)
Diffuse interface models of active living matter
12:30 — 14:00
Lunch
14:00 — 14:30
Giuseppe Zurlo (NUI Galway)
Micro-displacement tensor
14:30 — 15:00
15:00 — 15:30
Coffee break
15:30 — 16:00
Dec. 10, 2025
09:00 — 09:30
09:30 — 10:00
Georg Dolzmann (U of Regensburg)
Stress-modulated growth models
10:00 — 10:30
Alexander Erlich (CNRS -U Grenoble Alpes)
Incompatibility-driven growth
10:30 — 11:00
Coffee break
11:00 — 11:30
William Feldman (U of Utah, Saltlake City)
The pinning effect of dilute defects
11:30 — 12:00
12:00 — 12:30
19:00 — 22:00
Social dinner
Dec. 11, 2025
09:00 — 09:30
10:30 — 11:00
Coffee break
12:00 — 12:30
Alain Miranville (Université Le Havre Normandie)
The Cahn-Hilliard equation with a nonlinear source term
12:30 — 14:00
Lunch
14:00 — 14:30
15:00 — 15:30
Coffee break
Dec. 12, 2025
09:00 — 09:30
10:00 — 10:30
10:30 — 11:00
Coffee break
11:00 — 11:30
12:30 — 13:00
Lev Truskinovsky (PSL, Paris)
Generalized Clapeyron's Theorem
This event has no subevents associated to it.

Organizers

Name Affiliation
Serena Dipierro University of Western Australia
Julian Fischer Institute of Science and Technology Austria
Matteo Novaga University of Pisa
Elisabetta Rocca University of Pavia
Xavier Ros-Oton University of Barcelona
Ulisse Stefanelli University of Vienna
Enrico Valdinoci University of Western Australia

Attendees

Name Affiliation
Helmut Abels University of Regensburg
Abramo Agosti Universita degli Studi (Pavia)
Goro Akagi Tohoku University
Nuno Alves University of Vienna
Anton Arnold Vienna University of Technology
Costante Bellettini University College London
Verena Bögelein Paris-Lodron-Universität Salzburg
Alberto Bressan The Pennsylvania State University
Giovanni Brigati Institute of Science and Technology Austria
Claudia Bucur Università degli Studi di Milano
Sun-Sig Byun Seoul National University
Davide Carazzato University of Vienna
Jose Antonio Carrillo de la Plata University of Oxford
Michele Caselli Scuola Normale Superiore di Pisa
Giulia Cavalleri University of Pavia
Annalisa Cesaroni University of Padova
Antonin Chambolle CEREMADE University Paris Dauphine
Andrea Chiesa University of Vienna
Pasquale Ciarletta Politecnico di Milano
Pierluigi Colli University of Pavia
Anna Dall'Acqua University of Ulm
Apostolos Damialis European Mathematical Society
Elisa Davoli Vienna University of Technology
Luigi De Masi University of Trento
Guido De Philippis University of Padua, Padua, Italy
Antonio De Rosa Università Commerciale Luigi Bocconi
Georg Dolzmann University of Regensburg
Frank Duzaar Paris-Lodron-Universität Salzburg
Alexander Erlich CNRS - Université Grenoble Alpes
Alberto Fanizza TU Wien
Max Fathi Université Paris Cité
William Feldman University of Utah
Xavier Fernandez-Real École Polytechnique Fédéral de Lausanne
Enric Florit-Simon ETH Zürich
Irene Fonseca Carnegie Mellon University
Matteo Fornoni University of Milan
Takeshi Fukao Ryukoku University
Harald Garcke University of Regensburg
Noah Geltner Vienna University of Technology
Rossella Giorgio Vienna University of Technology
Michael Goldman CNRS & Ecole Polytechnique, Palaiseau
Maurizio Grasselli Politecnico di Milano
Sebastian Hensel University of Leipzig
Peter Hirvonen Vienna University of Technology
Jonas Ingmanns Institute of Science and Technology Austria
Ansgar Jüngel Vienna University of Technology
Aram Karakhanyan University of Edinburgh
Shokhrukh Kholmatov University of Vienna
Sunghan Kim Uppsala University
Konstantinos Koumatos University of Sussex
Dennis Kriventsov Rutgers University
Martin Kružík Czech Academy of Sciences
Anna Kubin TU Wien
Kota Kumazaki Kyoto University of Education
Mateusz Kwaśnicki Wroclaw University of Science and Technology
Kei Fong Andrew Lam Hong Kong Baptist University
Xavier Lamy Institut de Mathématiques de Toulouse
Robert Lasarzik Weierstrass Institute Berlin
Tim Laux Heidelberg University
Marta Lewicka University of Pittsburgh
Jiakun Liu University of Sydney
Luca Lombardini University of Vienna
Jan Maas Institute of Science and Technology Austria
Alice Marveggio Hausdorff Center for Mathematics, University of Bonn
Sara Merino-Aceituno University of Vienna
Alain Miranville Université Le Havre Normandie
Tatsuya Miura Kyoto University
Anastasia Molchanova TU Wien
Mihalis Mourgoglou Universidad del País Vasco
Yoshihito Nakajima Tohoku University
Francesco Nobili University of Pisa
Vicent Pallardó-Julià University of Vienna
Davide Parise Imperial College London
Dirk Peschka Weierstrass Institute Berlin
Alessandro Pigati Università Commerciale Luigi Bocconi
Alessandra Pluda University of Pisa
Andrea Poiatti University of Vienna
Annamaria Pollino Vienna University of Technology
Marco Pozzetta Politecnico di Milano
Paola Pozzi University of Duisburg-Essen
Mariya Ptashnyk Heriot-Watt University
Filippo Quattrocchi Institute of Science and Technology Austria
Samuele Riccò Vienna University of Technology
José Francisco Rodrigues University of Lisbon
Tomàś Roubíček Charles University Prague
Melanie Rupflin University of Oxford
Fabian Rupp University of Vienna
Alessandro Scapin Università degli Studi di Milano
Luca Scarpa Politecnico di Milano
Felix Schulze University of Warwick
Sebastian Schwarzacher Uppsala University
Daniele Semola University of Vienna
Joaquim Serra ETH Zurich
Wenhui Shi RWTH Aachen
Andrea Signori Politecnico di Milano
Lauro Silini Institute of Science and Technology Austria
Theresa Simon University of Münster
Nicola Soave University of Torino
Giacomo Enrico Sodini University of Vienna
María Soria-Carro Universidad Autonoma de Madrid
Salvatore Stuvard Università degli Studi di Milano
Jack Thompson University of Western Australia
Xavier Tolsa Autonomous University of Barcelona
Giuseppe Tomassetti University Roma Tre
Yoshihiro Tonegawa Institute of Science Tokyo
Lev Truskinovsky Univertsité PSL, Paris
Tobias Unterberger TU Wien
José Miguel Urbano King Abdullah University of Science and Technology
Gianmaria Verzini Politecnico di Milano
Andreas Vikelis University of Vienna
Christian Wagner Institute of Science and Technology Austria
Julian Walser University of Vienna
Gaoming Wang Beijing Institute of Mathematical Sciences and Applications (BIMSA)
Marvin Weidner Universität Bonn
Georg Weiss University of Duisburg-Essen
Hao Wu Fudan University
Jack Xin University of California, Irvine
Hui Yu National University of Singapore
Rada Ziganshina KTH Royal Institute of Technology
Giuseppe Zurlo National University of Ireland, Galway
Preview of Jack Thompson - The nonlocal halfspace theorem
Jack Thompson (UWA, Perth): The nonlocal halfspace theorem
Sept. 29, 2025 14:00 — 15:00
Preview of Dennis Kriventsov - Non-minimizing and min-max solutions to Bernoulli problems
Dennis Kriventsov (Rutgers U): Non-minimizing and min-max solutions to Bernoulli problems
Sept. 30, 2025 15:30 — 16:30
Preview of Marvin Weidner - Regularity for the nonlocal one-phase problem
Marvin Weidner (U of Bonn): Regularity for the nonlocal one-phase problem
Oct. 1, 2025 09:00 — 10:00
Preview of Mateusz Kwaśnicki - Liouville's theorems for Lévy operators
Mateusz Kwaśnicki (UST Wroclaw): Liouville's theorems for Lévy operators
Oct. 1, 2025 10:00 — 11:00
Preview of Jiakun Liu - Free boundary problems in optimal transportation
Jiakun Liu (U Sydney): Free boundary problems in optimal transportation
Oct. 2, 2025 11:00 — 12:00
Preview of María Soria-Carro - An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data
María Soria-Carro (U Autonoma de Madrid): An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data
Oct. 2, 2025 15:30 — 16:30
Preview of Yoshihiro Tonegawa - Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course, Part 2
Yoshihiro Tonegawa (Institute of Science Tokyo): Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course 2
Oct. 29, 2025 15:15 — 17:00
Preview of Yoshihiro Tonegawa - Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course, Part 3
Yoshihiro Tonegawa (Institute of Science Tokyo): Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course 3
Oct. 31, 2025 15:15 — 17:00
Preview of Yoshihiro Tonegawa - Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course, Part 4
Yoshihiro Tonegawa (Institute of Science Tokyo): Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course 4
Nov. 3, 2025 15:15 — 17:00
Preview of Yoshihiro Tonegawa - Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course, Part 5
Yoshihiro Tonegawa (Institute of Science Tokyo): Introduction to Brakke's Mean Curvature Flow, SRF Lecture Course 5
Nov. 5, 2025 15:15 — 17:00
Preview of Annalisa Cesaroni - Periodic tilings with minimal energy
Annalisa Cesaroni (U Padova): Periodic tilings with minimal energy
Nov. 10, 2025 11:00 — 11:40
Preview of Francesco Nobili - Isoperimetric planar Tilings with unequal cells
Francesco Nobili (U Pisa): Isoperimetric planar Tilings with unequal cells
Nov. 10, 2025 11:40 — 12:20
Preview of Antonio De Rosa - Rigidity of critical points of hydrophobic capillary functionals
Antonio De Rosa (U Bocconi, Milano): Rigidity of critical points of hydrophobic capillary functionals
Nov. 10, 2025 14:00 — 14:40
Preview of Sebastian Schwarzacher - Regularity estimates of a fluid-free surface evolution
Sebastian Schwarzacher (Uppsala U): Regularity estimates of a fluid-free surface evolution
Nov. 10, 2025 15:45 — 16:15
Preview of José Francisco Rodrigues - On Minimal and Capillary Surfaces with Bounded Slopes
José Francisco Rodrigues (U Lisbon): On Minimal and Capillary Surfaces with Bounded Slopes
Nov. 11, 2025 09:40 — 10:20
Preview of Michael Goldman - Variational models for charge liquid drops
Michael Goldman (CNRS & Ecole Polytechnique, Palaiseau): Variational models for charge liquid drops
Nov. 11, 2025 11:00 — 11:40
Preview of Marco Pozzetta - Quantitative isoperimetric inequalities in capillarity problems
Marco Pozzetta (Politecnico Milano): Quantitative isoperimetric inequalities in capillarity problems
Nov. 11, 2025 11:40 — 12:20
Preview of Luigi De Masi - Regularity of capillary minimal surfaces
Luigi De Masi (U of Trento): Regularity of capillary minimal surfaces
Nov. 11, 2025 14:00 — 14:40
Preview of Lauro Silini - Stability of spheres in the Complex Hyperbolic Space
Lauro Silini (ISTA, Klosterneuburg): Stability of spheres in the Complex Hyperbolic Space
Nov. 11, 2025 14:40 — 15:20
Preview of Anna Dall'Acqua - On the free boundary elastic flow
Anna Dall'Acqua (U Ulm): On the free boundary elastic flow
Nov. 12, 2025 09:00 — 09:40
Preview of Shokhrukh Kholmatov - Crystalline elastic flow of polygonal curves
Shokhrukh Kholmatov (U of Vienna): Crystalline elastic flow of polygonal curves
Nov. 12, 2025 11:00 — 11:40
Preview of Salvatore Stuvard - The epsilon-regularity theorem for Brakke flows near triple junctions
Salvatore Stuvard (U degli Studi di Milano): The epsilon-regularity theorem for Brakke flows near triple junctions
Nov. 13, 2025 09:40 — 10:20
Preview of Xavier Lamy - Minimality of the Hopf map for the Faddeev-Skyrme energy
Xavier Lamy (IMT, Toulouse): Minimality of the Hopf map for the Faddeev-Skyrme energy
Nov. 13, 2025 11:40 — 12:20
Preview of Theresa Simon - Linear stability of the self-similarly shrinking lens
Theresa Simon (U Münster): Linear stability of the self-similarly shrinking lens
Nov. 13, 2025 14:40 — 15:20
Preview of Maurizio Grasselli - Convergence to equilibrium of weak solutions to Cahn-Hilliard equations
Maurizio Grasselli (Politecnico Milano): Convergence to equilibrium of weak solutions to Cahn-Hilliard equations
Dec. 9, 2025 10:00 — 10:30
Preview of Giuseppe Zurlo - Micro-displacement tensor
Giuseppe Zurlo (NUI Galway): Micro-displacement tensor
Dec. 9, 2025 14:00 — 14:30
Preview of Martin Kružík - The effects of pressure loads in the dimension reduction of elasticity models
Martin Kružík (Czech Academy of Sciences, Prague): The effects of pressure loads in the dimension reduction of elasticity models
Dec. 9, 2025 14:30 — 15:00
Preview of Luca Scarpa - Uniqueness by noise and doubly nonlinear evolution equations
Luca Scarpa (Politecnico Milano): Uniqueness by noise and doubly nonlinear evolution equations
Dec. 9, 2025 15:30 — 16:00
Preview of Elisa Davoli - Accretive growth for elastic solids
Elisa Davoli (TU Vienna): Accretive growth for elastic solids
Dec. 10, 2025 09:00 — 09:30
Preview of Alexander Erlich - Incompatibility-driven growth
Alexander Erlich (CNRS -U Grenoble Alpes): Incompatibility-driven growth
Dec. 10, 2025 10:00 — 10:30
Preview of William Feldman - The pinning effect of dilute defects
William Feldman (U of Utah, Saltlake City): The pinning effect of dilute defects
Dec. 10, 2025 11:00 — 11:30
Preview of Giulia Cavalleri - On a nonisothermal tumor growth model of Caginalp type
Giulia Cavalleri (U of Pavia): On a nonisothermal tumor growth model of Caginalp type
Dec. 10, 2025 11:30 — 12:00
Preview of Andrea Signori - Dynamics of Active Droplets: From Self-Organization to Division
Andrea Signori (Politecnico Milano): Dynamics of Active Droplets: From Self-Organization to Division
Dec. 10, 2025 12:00 — 12:30
Preview of Helmut Abels - Local well-posedness of to the Cahn–Hilliard–Biot System
Helmut Abels (U of Regensburg): Local well-posedness of to the Cahn–Hilliard–Biot System
Dec. 11, 2025 09:00 — 09:30
Preview of Alain Miranville - The Cahn-Hilliard equation with a nonlinear source term
Alain Miranville (Université Le Havre Normandie): The Cahn-Hilliard equation with a nonlinear source term
Dec. 11, 2025 12:00 — 12:30
Preview of Mariya Ptashnyk - Multiscale modelling and analysis of growth of biological tissues
Mariya Ptashnyk (Heriot-Watt U, Edinburgh): Multiscale modelling and analysis of growth of biological tissues
Dec. 12, 2025 10:00 — 10:30
Preview of Harald Garcke - Two-phase Navier–Stokes flow with viscoelasticity
Harald Garcke (U of Regensburg): Two-phase Navier–Stokes flow with viscoelasticity
Dec. 12, 2025 11:00 — 11:30
At a glance
Type:
Thematic Programme
When:
Sept. 29, 2025 — Dec. 19, 2025
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Serena Dipierro (UWA, Perth)
Julian Fischer (ISTA, Klosterneuburg)
Matteo Novaga (U Pisa)
Elisabetta Rocca (U of Pavia)
Xavier Ros-Oton (U of Barcelona)
Ulisse Stefanelli (U of Vienna)
Enrico Valdinoci (UWA, Perth)