This Toppforsk@IE research group consists of members from the Department of Mathematical Sciences. The group has three research goals: systems with shocks and singularities (in particular mean field games), stochastic partial differential equations, and computer-assisted proofs.
Systems with shocks and singularities. We seek solution concepts that allow continuation of solutions beyond sudden changes in the qualitative behaviour. Examples are the development of shocks or wave breaking in water waves, or the transition between finitely and infinitely many particles or agents. The latter appears in so-called mean field games which investigates the transition between continuum models. This direction of investigation bridges the group's current expertise with some new areas where it can be applied.
Stochastic partial differential equations. This type of differential equations has become a hot topic in recent years as its theoretical development is essential in the common ground between statistics and mathematics. It also plays a major role in disiplines with large data sets such as neuroscience and biologi. The group has started pursuing this direction, and intends to broaden its understanding of the topic.
Computer-assisted proofs. A recently developed new tool in mathematics which has, combinded with analytical theory, given surprising and major break throughs within areas where fine or precise estimates are needed, e. g. in fluid mechanics. The tool is not yet exploited in Norway, and the group believes it can be of great use to the community.
