Research methods
The research methodology to be adopted is strongly problem oriented
although, despite the diversity of the selected problems, many methodological questions go far beyond not only
the level of a single group of problems but also the level of the central themes of this proposal (front
propagation and singularities). The selected problems need to be defined very precisely,
broken up into smaller pieces, and studied in relatively small groups comprising both young researchers and
highly experienced team members. The Steering Committee, consisting of the team coordinators and a
training coordinator, will play an active role in this process and will continuously check the
efficiency of the research method, giving particular importance to the following features.
Applications.
The role of applications is crucial in most of the
selected problems and experts in the specific fields of application, belonging either to one of the teams
or having intensive collaborations with the teams, will be actively involved to monitor the
relevance of the research activity to applications.
Interdisciplinary approach.
Almost all selected problems require a
strongly interdisciplinary
approach and expertise from different mathematical fields such as analytical PDE theory, formal
asymptotics, geometric measure theory, numerical analysis and mathematical modelling. The
composition of the groups in which the problems are studied will reflect the different scientific requirements.
Flexibility.
High level problem solving is a dynamic activity and requires a certain amount of
flexibility concerning the choice of topics, at least within each group of
problems. Flexibility is a characteristic of most good applied mathematics:
the absence of expensive experimental machinery and the universality of mathematical
methods make it possible tomaximise the advantage of not having severe research
constraints. Obviously, such flexibility has tobe compatible with the general
goals of the proposal.