For the next five-year period it is important that the most successful CMA research activities are extended. During the Centre of Excellence-period the research groups in stochastic analysis and partial differential equations have been strengthened and the activity has been substantially increased. Both groups were characterized as excellent in the recent evaluation done by NFR. In the field of geometry new research activities have been created at the interface between computational mathematics and more classical disciplines. Furthermore, when CMA is integrated into MI we will focus on research that strengthens collaboration with the other existing research groups at MI. There is a significant potential for such collaboration with the groups in e.g. algebra, analysis, statistics and mechanics. Most likely this will improve the overall quality of the department. More detailed plans for the research activity in stochastic analysis, partial differential equations and geometry will be presented in the section "Subprojects" below.
When the SFF period of the CMA expired in 2013, the group in computational mathematics at CMA were moved from IFI to MI. As a consequence, MI have taken responsibility for the research fields in mathematics which are of major importance for modern computer technology and software. For example, combinatorics is a classical mathematical area, often associated with algebra, which in recent decades has generated considerable interest, partly due to its impact on the design of algorithms for
large discrete structures in areas like search engines, internet and computer network. Moreover, combinatorics plays an important role in life science (e.g. DNA sequencing, ecological networks etc.). CMA already has some research activity in combinatorics and optimization, and MI should therefore consider the possibility of increasing the focus on this topic in the coming years.
The CMA research strategy is based on certain criteria and viewpoints. In addition to extend and improve the most successful parts of the existing research activities, CMA will focus on strategic research areas of major national and international importance and work on problems that have major potential for applications in science and technology. Finally, it is important to keep a balance between pure theoretical activities and more applied research. The strength of mathematics is its generality, and this potential will easily be lost if all the research is targeted at specific applications. As a result of these considerations, we have decided to focus on applications in two important areas, mathematics for life sciences and energy and climate research. Our vision is that these topics represent mathematical research with increasing importance in the years to come. It is the responsibility of the leadership of the CMA to play an active role in organizing workshops, research groups and applications to grants and programs. In particular, such activities targeted to projects in life sciences and energy research will have the highest priority.
The last decade has seen an unprecedented development in biology and medicine. Furthermore, computations and mathematical models are playing an increasingly important role in these branches of science. CMA will increase its focus on applications of mathematics for life sciences in the coming years. The UiO has the leading school of medicine in Norway and a large biology department with a number of excellent research groups. We believe that many of these groups will benefit from more interactions with mathematical research, and together with statistics, CMA has the basic mathematical profile needed for such interdisciplinary projects. However, as models become more complex, most branches of mathematics may play a role here, and we can probably even expect that new fields of mathematics will arise from interaction with the life sciences.
Research oriented towards energy and climate is very important internationally and expected to be even more important in the future. Energy and climate is one of the strategic research directions at the UiO, and major research programs exist at national and EU level. The research at CMA has already a strong focus on energy and weather markets analysis based on stochastic analysis. However, there is a huge potential for an even wider contribution from CMA. Market integration and introduction of new sources of electricity production like wind power and solar energy has created many new challenges involving sophisticated mathematics. For example, the mathematical modeling of turbulence in a wind farm requires the development of delicate physical, statistical and numerical methodology. Another example is the optimal design of wind farms, which may be different off-shore than on-shore. This is of vital importance for the development of the wind power industry, both nationally and internationally. To solve such questions, theory from mechanics, partial differential equations, optimization theory, numerical analysis and stochastics will play an important role. By joining forces with other groups at MI, CMA has the platform for an integrated approach to solve challenging problems in energy and climate research.