Theme Sessions

1  Regularity and Singularity of Free Boundaries

Organizers: Henrik Shahgholian and Erik Lindgren

The aim of this session is to present both coherent and diverse approaches to the regularity theory of free boundary problems. The invited speakers have expertise within the analysis of regular and singular points of various free boundary problems. Their areas of expertise encompass for instance the thin obstacle, non-local problems and the Mumford-Shah functional. We have focused on giving younger researchers the possibility to present their research.

Invited Speakers:

    Wenhui Shi (University of Coimbra, Portugal)

    Xavier Ros-Oton (University of Texas at Austin, USA)

    Dennis Kriventsov (Courant Institute, New York University, USA)

    Luca Lombardini (University of Milan, Italy)

    Hayk Mikaelyan (University of Nottingham, Ningbo, China)

    Karen Yeressian (Royal Institute of Technology (KTH), Stockholm, Sweden)

    Ryan Hynd (University of Pennsylvania, USA)

2  Phase Field Models

Organizers: Harald Garcke and Elisabetta Rocca

Phase field models are a versatile approach to approximate free boundary problems. New applications of phase field methods e.g. in two-phase flow and tumor growth will be discussed. This theme session will concentrate on recent results on the mathematical analysis of phase field methods.

Invited Speakers:

    Helmut Abels (University of Regensburg, Germany)

    Sergio Frigeri (Universita Cattolica del Sacro Cuore, Italy)

    Kei Fong Lam (University of Regensburg, Germany)

    Antonio Segatti (University of Pavia, Italy)

3  Free Boundary Problems in Biology

Organizer: Avner Friedman

The biological questions are concerned with biomedical issues that arise in the human artery that goes from the heart to the main body. This artery may become clogged by fat, called plaque, resulting in heart attack, or may lose it elastic properties and collapse leading to instant death. This session will deal with such events with rigorous analysis as well as numerical aspects.

Invited Speakers: 

    Leonid Berlyand (The Penn State University, USA)

    Bei Hu (University of Notre Dame, USA)

    Wenrui Hao (Pennsylvania State University, USA)

    Nicolas Meunier (Paris Descartes University-Paris V, France)

4  Free Boundary Problems in Gas Dynamics, MHD and Related Topics

Organizers: Yachun Li, Dehua Wang and Weike Wang

This session brings together experts in the area of free boundary problems in gas dynamics, MHD and related topics to exchange new results and ideas, to explore new research directions and topics in analysis and applications, and to foster new collaborations and connections.

Invited Speakers:

    Seung-Yeal Ha (Seoul National University, Korea)

    Ming Mei (McGill University, Canada)

    Ronghua Pan (Georgia Institute of Technology, USA)

    Tong Yang (City University of Hong Kong, China)

5  Surface PDEs and Related Topics

Organizers: Charlie Elliott and Vanessa Styles

Surface PDEs arise in a wide variety of applications including fluid dynamics, biological systems and materials science.  This session will focus on state-of-the-art of analytical and numerical methods for studying models involving surface PDEs. Topics will include PDEs on evolving surfaces and coupling to bulk processes.

Invited Speakers:

    Charlie Elliott (University of Warwick, UK)

    Robert Nurnberg (Imperial College London, UK)

    Vanessa Styles (University of Sussex, UK)

    Chandrasekhar Venkataraman (University of St Andrews, UK)

6  Free Boundary Problems in Mixed-type PDEs

Organizers: Mikhail Feldman and Wei Xiang

Analysis of steady and self-similar shocks in problems of gas dynamics leads to study of free boundary problems for PDE of mixed elliptic-hyperbolic type. This theme session will present recent developments in this area.

Invited Speakers:

    Feimin Huang (Chinese Academy of Sciences, China)

    Myoungjean Bae (Pohang University of Science and Technology, Korea)

    Chunjing Xie (Shanghai Jiao Tong University, China)

    Jun Chen (Southern University of Science and Technology, China)

7  Probabilistic Methods for Free Boundary Problems through Reflected Backward Stochastic Differential Equations

Organizers: Shige Peng and Lihe Wang

We focus on the connections of the reflected solutions of backward SDE with free boundary problems toward theoretical and applied purposes.

Invited Speakers:

    Shige Peng (Shandong University, China)

    Ying Hu (Universite de Rennes 1, France)

    Hanwu Li (Shandong University, China)

    Zhongming Qian (Exeter College, University of Oxford, UK)

8  Optimization and Control of Interfaces

Organizers: Michael Hinze and Michael Hintermuller

This theme session covers mathematical research in optimization and control of interfaces ranging from numerical analysis and adaptive concepts over algorithm design to the tailored treatment of optimization applications with free boundaries. It thereby forms a platform and fair for the exchange of ideas among young researchers and leading experts in the field, and for fostering and extending international collaborations between research groups, in particular with groups from the rapidly emerging Chinese control and optimization community.

Invited Speakers:

    Lubomir Banas (University of Bielefeld, Germany)

    Michael Hintermueller (Weierstrass Institute for Applied Analysis and Stochastics, Germany)

    Tobias Keil (Humboldt- Universität zu Berlin, Germany)

    Andrew Lam (University of Regensburg, Germany)

9  Free Boundary Problems in Water Waves, Incompressible Fluids and Related Topics

Organizers: Zhen Lei and Chunjing Xie

This session brings together experts in the area of free boundary problems in water waves, incompressible fluids and related topics to exchange new results and ideas, to explore new research directions and topics in analysis and applications, and to foster new collaborations and connections.

Invited Speakers:

    Masashi Aiki (Tokyo University of Science, Japan)

    Xumin Gu (Shanghai University of Finance and Economy, China)

    Chengchun Hao (Chinese Academy of Sciences, China)

    Xin Liu (The Chinese University of Hong Kong, China)

10  Free Boundaries/Interfaces on Graphs

Organizer: Yves van Gennip

While many free boundary problems are formulated in a continuum space, in certain contexts free interfaces arise on discrete structures. Examples range from lattice growth and sandpile models to PDE-like interface models in image and data analysis. This mini symposium gathers experts working on all these various different types of free boundary problems on graphs.

Invited Speakers:

    Hayk Aleksanyan (Royal Institute of Technology (KTH), Stockholm, Sweden) 

    Abderrahim Elmoataz (University of Caen Basse Normandie, France)  

    Yves van Gennip (University of Nottingham, UK)

    Matthew Thorpe (Carnegie Mellon University, USA)

    Xiaoqun Zhang (Shanghai Jiao Tong University, China)

11  Numerics for Free Boundary Problems and Related Topics

Organizer: Robert Nurnberg

The numerical solution of free boundary problems (FBPs) remains a challenge, and often requires novel approaches to design robust, efficient and accurate numerical methods. The goal of this theme session is to bring together researchers working on different applications featuring FBPs and to present approaches for their numerical solution.

Invited Speakers:

    Luca Dede (Ecole polytechnique federale de Lausanne, Switzerland)

    Aymen Laadhari (The Computer Vision Laboratory, ETH Zurich, Switzerland)

    Maxim A. Olshanskiy (University of Houston, USA)

    Shawn Walker (Louisiana State University, USA)

12  Free Boundary Problems in Industry

Organizer: John Ockendon, Song Jiang and Yichao Zhu

This session is aimed to promote the inter-communication between academia and industry on free-boundary problems that have arisen in various industrial sectors. For this purpose, this session is expected to bring about discussion from the following three angles: 1) experience sharing on previous success in resolving industrial free-boundary problems; 2) introduction of existing (industrial) challenges that display a free-boundary nature (mainly by industrial representatives); 3) presentation of ongoing industrial projects where difficulties of free-boundary type come up (mainly by academic representatives). It is highly desired that tentative industrial-academic collaborations can be catalyzed and strengthened by the proposed session.

Invited Speakers: 

    Huaxiong Huang (York University, Canada)

    Lihua Lv (Bao Steel, China)

    John Ockendon (University of Oxford, UK)

    Hong-Ming Yin (Washington State University, USA)

13  Further Connections with Other Areas

Organizers: Jose Francisco Rodrigues and Juan Luis Vazquez

The context and the connections of free boundary problems are multiple and evolve with time. In this session we collect recent views and novel results on actual subjects that open connections with crystal growth, where the role of non-smooth anisotropy rises difficult issues, with shape optimisation problems with functionals that relate to nonlocal competing interactions, and with other types of nonlocal effects in interphases and in interfaces that require deep analysis and new developments in the growing theory of fractional Laplacian type operators.

Invited Speakers:

    Antonin Chambolle (Ecole Polytechnique, France)

    Ki-Ahm Lee (Seoul National University, Korea)

    Yannick Sire (Johns Hopkins University, USA)

    Hugo Tavares (University of Lisboa, Portugal)


14  PDE Problems with Moving and Free Boundaries

Organizers: Leonid Berlyand, Lei Zhang and Wenrui Hao

Both theoretical and computational techniques have recently developed to study the partial differential equation (PDE) with a free boundary such as tumor growth, cardio-vascular diseases and cellular biology. This theme session will explore recent theoretical and computational methods for solving free boundary problems which arises from biology, medical science and engineering. This theme session will invite some experts in this field to present current studies in solving free boundary systems. Recent progress on computational methods to solve nonlinear differential equations related to moving boundaries will be also included in this theme session.

Invited Speakers:

    Leonid Berlyand (The Penn State University, USA)

    Harunori Monobe (Tokyo Institute of Technology, Japan)

    Nicolas Meunier (Paris Descartes University-Paris V, France)

    Qi Wang (University of South Carolina, USA)

    Peng Zhang (Shanghai Jiao Tong University, China)

15  Nonlocal Nonlinear PDEs and Free Boundary Problems

Organizers: Serena Dipierro and Luca Lombardini

The session aims at gathering together some very distinguished researchers in the fields of free boundary problems, with possible applications to nonlinear phenomena and nonlocal equations. The event could take into account several aspects of the regularity theory, the qualitative and quantitative behavior of the solutions, the geometric evolution of the interfaces, the symmetry and classification properties of solutions and free boundaries, also in connections with classical problems in spectral theory and with possible applications to concrete models, such as optimal insulation and reinforcement problems.

Invited Speakers:

16  Free Boundary Problems in Finance

Organizer: Jin Liang

Now researches about free boundary on finance have been extended in many areas, such as pricing and calculation on different American style products, optimal strategy on buying/selling stocks or paying divided, management of investment and consumptions, control credit risks such as default and credit rating migration etc. To modelling these financial problems in the real world, many new and interesting free boundary problems were derived. There are free boundary problems of both theoretical and practice significances. We hope to get together of experts working on the free boundary problems in finance. We will exchange ideas, latest achievements and newest problems.

Invited Speakers:

    Xinfu Chen (University of Pittsburgh, USA)

    Min Dai (National University of Singapore, Singapore)

    Fahuai Yi (South China Normal University, China)

    Jianwei Lin (Putian University, China)

17  Variational and Quasi-Variational Inequalities with Gradient Constraints and Related Problems

Organizers: Carlos N. Rautenberg and Lisa Santos

The theme session aims to bring together senior experts and young scientists making contributions in variational and quasi-variational inequalities with gradient constraints and related problems. In particular this session is intended to develop discussion on two main points: 1) Challenges involving new models in electromagnetostatic, thermohydraulics, and thick fluids, among others and 2) New mathematical techniques arising when dealing with such non-smooth and non-linear phenomena. We further expect to foster new ideas in the treatment of these problems and develop connections among researchers of the community.

Invited Speakers:

    Nobuyuki Kenmochi (University of Warsaw, Poland and Chiba University, Japan)

    Takeshi Fukao (Kyoto University of Education, Japan)

    Ryan Hynd (University of Pennsylvania, USA)

    Mohammad Safdari (Institute for Research in Fundamental Science, Iran)

    Lisa Santos (University of Minho, Portugal)

    Carlos N. Rautenberg (Humboldt-Universität zu Berlin, Germany)