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Limit problems in Analysis
The focus of this workshop will be on the combination of so-called "formal" and rigorous methods in applied analysis. Limit problems are ubiquitous in mathematical models and also in more "pure" analysis of PDEs. On the one hand, an application may dictate that a particular parameter in the problem is small (or large). On the other hand, the system may, itself, evolve in such a way that it approaches some limit problem, as time tends to infinity or as it approaches a singularity in its dynamics. In these asymptotic limits the problem reduces to a simpler problem, at least formally.
The word "formal" indicates that these asymptotic techniques are often without proof or rigorous justification in the mathematical sense, though they are widely used and universally accepted in physics. They thus present a challenge to mathematicians. Vice versa, rigorous proofs do not just validate formal derivations, but they also lead to a better understanding of why the formal methods work.
The challenge is to get the best of both worlds, or to at least take advantage of the overlap between formal and rigorous approaches in order to progress both fields and to answer a variety of questions. For a particular ``pure'' problem, what applicable formal methods are out there? Could they be applied to a novel type of problem? Which problems from pure mathematics should first be attacked through formal techniques? What numerical approaches are required? How reliable are the formal methods? Which
formal results are so interesting that they warrant a rigorous proof? Can the formal solutions give a hint about a method for rigorous justification?
Our aim is to bring together a group of young mathematicians, some of them with a rigorous background, others with a more formal training. They could have expertise in a particular field (rigorous, formal or applied) or be interested in combining rigorous and formal approaches. There should be plenty of opportunity for interactions and colla-borations. Additionally, we invite a smaller number of more senior researchers working in these fields.