Mathematics is a fundamental subject in which we offer many courses at Mid Sweden University; from first-cycle courses in teacher education programmes and various engineering programmes up to third-cycle courses for our doctoral students in Mathematics. This means that not only different levels need to be met, but also that different parts of and approaches to the subject are needed. This intrinsic width is also well reflected in our research, which includes both pure and applied mathematics.
Research groups
We have four research groups covering well-selected areas of study, ranging from strongly application inclined numerical analysis to more purely mathematical directions such as complex analysis. There in between we find groups working with differential equations connected to mathematical physics and multiscale analysis, which involves both real world application and development of new theoretical results of independent mathematical interest. The groups have many collaborators nationally and internationally. Together with a network of internal connections, within the subject as well as with other subjects, mathematics contributes to the theoretical level in important applications, as well as progress within the subject itself.
Complex analysis
This group, which is led by Professor Egmont Porten, directs its research towards open questions in geometry of Stein manifolds, CR geometry and differential equations with complex coefficients. The group is well established within its field, and is closely integrated in a network of similar groups at universities in the Nordic countries, but it also has numerous research–in-pair projects with scientists from well-known universities all over Europe.
Differential equations and multiscale analysis
The research primarily deals with mathematical homogenization theory. This branch of mathematics builds on ideas inspired by problems appearing while studying heterogeneous media with a complex structure. The mathematical fundaments are functional analysis and Sobolev space based theory of partial differential equations. Many applications are found in solid and fluid mechanics and modern physics. Among new promising directions study of human cell dynamics could be mentioned, which among other things study how muscle cells and neurons work and interact. This group is led by Professor Anders Holmbom.
Applied scientific computing
Research in applied scientific computing is conducted in a cross-disciplinary group – Computational Mathematics and Physics (CoMP), led by Professor Per Edström. Current areas of research include the radiative transfer problem, multi-body problems and solid mechanics of fibre-based materials; a majority of the publications appearing in various physics journals. The group works in close cooperation with other research groups on applied and industrial problems, and is very successful in raising external funding.
Mathematical physics
The main area of research is integrable systems, one of the most active topics in modern mathematical physics with many applications. This work aims to develop structural understanding of these systems, many of them referred to as soliton equations, like the Korteweg-de Vries or the Nonlinear Schrödinger equation, but also to construct and do qualitative studies of solution classes.