Free Boundary Problems 2026

Scientific Programme

Thematically, the conference will cover a broad range of topics from modeling, analysis, optimization to numerical realization. These include aspects such as uncertainties or stochastics, data-driven intelligent numerical solution techniques (e.g. utilizing techniques of machine learning), and applications.

Plenary Talks

PL

Contributed Talks

CS

Minisymposia

Parallel minisymposia at FBP.

• Degenerate PDEs and Free Boundary Problems

  MS-1

• Geometric Flows and Evolving Free Boundaries

  MS-2

  This minisymposium is focused on recent advances in the analysis of geometric flows and evolving free boundaries. A particular emphasis lies on the underlying gradient flow structure of such problems and how one capitalizes on it for rigorous analysis. The minisymposium brings together an international group of researchers, new and established, to discuss topics covering a representative range of mathematical questions and state-of-the-art techniques for geometric flows. These include, but are not limited to, weak and strong solution theories, quantitative relaxation to equilibrium, and effective geometric motion through random obstacles.

• Numerical Methods for Geometric PDEs

  MS-3

• Optimization and Free Boundaries

  MS-4

• Free Boundaries in Shape Optimization

  MS-5

• Hydrodynamic Models with Moving Contact Lines

  MS-6

• Phase Field Methods in Real-World Applications

  MS-7

  Phase field methods have become an important mathematical tool for modeling interfacial phenomena in a wide range of scientific and engineering applications. Their diffuse-interface nature makes them particularly suitable for problems involving evolving geometries, topological changes, and coupled multiphysics effects, as they arise for instance in materials science, fracture mechanics, geophysics, multiphase flow, biological systems, medical application, electrochemistry, and additive manufacturing.
  This mini-symposium is devoted to the mathematical analysis and application-driven development of phase field models. Topics of interest include well-posedness, regularity, stability, thermodynamic consistency, and the analysis of numerical approximations. Special attention will be given to models motivated by real-world problems and to the mathematical challenges arising from coupling mechanisms, nonlinear effects, complex geometries, and multiscale phenomena.
  The mini-symposium aims to provide a forum for researchers working on rigorous analytical foundations, numerical analysis, and realistic applications of phase field methods, with the goal of strengthening the connection between mathematical analysis and Real-World Applications.

• Phase Transitions and Pattern Formation

  MS-8

• Fluid-structure Interactions

  MS-9

  Fluid‑structure interaction (FSI) problems form a central class of coupled partial differential equation systems where the evolution of a viscous/inviscid incompressible/compressible fluid is directly linked to the dynamics of an elastic or viscoelastic solid and the interface separating them. These interactions pose fundamental analytical challenges due to nonlinear coupling across moving domains, free boundary motion, and multiphysics effects such as porous media, thermal coupling, and contact formation. This minisymposium brings together leading contributions that address these challenges from the perspectives of existence, uniqueness, regularity, stability, and singular limits for FSI models, as well as numerical and computational frameworks faithful to the underlying continuum mechanics.

• Free Boundaries in Biology

  MS-10

• Thin Material Structures

  MS-11

• Free Boundaries in Active Matter

  MS-12

• Free Boundary Problems in Data Science and Machine Learning

  MS-13

  This minisymposium gathers researchers from different career levels interested in synergies between free boundary problems and machine learning. On one hand, this encompasses the use of machine learning tools like operator learning for deriving efficient and versatile numerical schemes to approximate the solution of free boundary problems like the mean curvature flow. On the other hand, it involves the mathematical analysis of geometric problems arising in machine learning algorithms. For example, this kind of analysis can provide mathematical justification for graph clustering or robust classification algorithms using neural networks. The aim of the minisymposium is to present recent developments to a mathematically diverse audience, connect and exchange ideas with the free boundary community, and spark discussions about future collaborations.?

• Pattern Formation, Interfaces, and Free Boundary Problems

  MS-14

  This minisymposium focuses on recent mathematical advances at the intersection of the Calculus of Variations, Geometric Measure Theory, and Nonlinear Partial Differential Equations, with a strong emphasis on free boundary problems and interface dynamics. The session aims to bring together different analytical perspectives to discuss cutting-edge techniques for modeling and understanding these phenomena. Key topics include the regularity of free boundaries and energy minimizers, and the geometric analysis of local and non-local variational models for pattern formation.