The main vision
We want to create a national research centre in mathematics where
top class scientists from different areas can work together with
a joint prospectus and common goals. The main focus will be on mathematics
motivated from applications, with emphasis on problems arising from
modern scientific computing. Our belief is that the structure of
a centre like this will provide new fruitful collaborations and
lead to progress in research areas of importance to science, industry,
finance, and society in general. The centre will provide a new,
original, and innovative scientific environment for mathematical
research in Norway.
We firmly believe that ground-breaking research will depend on
strong links between theory and applications. Classical theorists
and numerical analysts with a strong commitment to theory will be
merged in the centre, the main focus being on topics which can lead
to the future development of computational mathematics. We also
believe that it is of fundamental importance that part of the research
group has a background in scientific disciplines other than mathematics.
The activity will be built upon four pillars represented by different
research areas, geometry, stochastic analysis, differential equations,
and applications in the physical sciences. These areas all represent
strong activities at the University of Oslo today. However, our
vision is that strong interaction between these fields will create
a leading group in mathematics for applications. We believe that
significant progress will arise as a result of a balance between
theory, computation, and applications.
The centre plans to organize workshops and symposia together with
industry, where new developments in mathematics and its applications
are presented. This will mainly be done through our close cooperation
with SINTEF Applied mathematics. The aim is to bridge the gap between
novel results in basic research and their use in potential technological
innovations. We also hope to expose essential new research directions
in close collaboration with industry.
In addition to the research itself, a major purpose of the centre
will be the training of new researchers. This will not be a new
situation for the members of the centre, since they have successfully
supervised a large number of candidates during the past two decades.
Based on the idea of combining theoretical mathematics with a wide
range of applications, the centre will create an ideal atmosphere
for research education in areas of practical importance for the
future. Hence, a main “product” of the centre will be
a large number of new researchers, trained and inspired by international
experts, in an exciting and stimulating environment. Their future
contributions to society, both in industry and in the research sector,
will represent important benefits of the centre.
The Research Group
The research activity will be built around ten principle investigators.
Eight of them hold full time positions at the University of Oslo,
one has his ordinary position at the Norwegian University of Science
and Technology (NTNU) in Trondheim, and one is a leading investigator
at SINTEF Applied mathematics. In addition to these ten, a number
(10-15) of other investigators, either from the University of Oslo
or other institutions, will be associated to the centre.
The principal investigators are:
Tom Lyche, Dept. of informatics, UiO
Ragni Piene, Dept. of mathematics, UiO
Tor Dokken, SINTEF Applied mathematics
Bernt Øksendal, Dept. of mathematics, UiO
Fred Espen Benth, Dept. of mathematics, UiO
Helge Holden, Dept. of mathematical sciences, NTNU
Ragnar Winther, Dept.s of informatics and mathematics, UiO
Geir Ellingsrud, Dept. of mathematics, UiO
Morten Hjorth-Jensen, Dept. of Physics, UiO
Mats Carlsson, Institute of theoretical astropysics, UiO
Lyche, Piene, and Dokken will be heading the activity in geometry.
Øksendal and Benth are the the pricipal investigators in
stochastic analysis. Holden and Winther both work with differential
equations, while Ellingsrud will focus on the interplay between
geometry, differential equations, and physics. Finally, Hjorth-Jensen
and Carlsson will represent the physical sciences.
Planned centre activities
The centre participants, as well as the centre itself, will contribute
to, participate in, or arrange a number of conferences, workshops,
educational programs, international networks etc. At present time
we only have partial overview of this activity, and we will have
to return to a more specific list later in annual reports and plans.
However, we will specifically mention that during 2003 we will
arrange a conference which will focus on the interdisciplinary aspects
of our research activity. The purpose of the conference is to strengthen
the ties between the different pillars, to further identify the
main research problems, and to improve the relations with key international
researches. We will regard this as a “kick-off”- event,
and we intend to invite some major international speakers. A “follow-up”
conference will be arranged two or three years later with the purpose
of returning to most of the same topics, evaluating the progress
in these areas.
Our research plan are divided into four main projects, roughly
representing the four pillars of the centre. However, each project
is composed of a variety of challenging research problems (subprojects),
and most of them require interactions from at least one of the other
pillars. We can only expect full activity in some of the subprojects.
At the present time it is not desirable to choose which subprojects
that will be given full priority. This will depend on, at least
partially, the interests and qualifications of the candidates recruited
for the Ph.D. stipends and post.doc. positions.
Anyway, successful attempts to attack the projects should lead
to the development of a research group with highest international
standards in modern applied mathematics, in particular in the direction
of computational mathematics. The creation of such a research group
in Norway can be seen as the ultimate goal of the Centre.
The Departments of Mathematics and of Informatics at the University
of Oslo are currently making sweeping changes in the way computional
mathematics is being taught. In the last years, several new basic
mathematics courses, which combine traditional calculus and programming,
have been taught, and more courses are being added. An entirely
new educational programme leading to Bachelor, Master, and Ph.D.
degrees in “Applied Mathematics and Scientific Computing”
started in the autumn of 2002.
This newly established educational programme entails the development
of a series of new courses which combine mathematics, computer science,
and applications to the physical sciences. One of our aims is the
development of a national graduate curriculum which encompasses
the newly established programme. We already offer permanent advanced
courses in partial differential equations, functional analysis,
numerical analysis, Monte Carlo methods, stochastic differential
equations, spline methods, algebraic geometry, and more. In addition,
we plan to establish courses in computational physics and fluid
mechanics, specific courses on modern tools within high-performance
computing, such as the use of parallel algorithms and machines,
advanced use of object-oriented languages in numerical projects,
and so on.
The combination of such an extensive graduate programme and the
research activity is expected to provide excellent educational and
training possibilities for graduate students (as well as for post-doctoral
fellows, visitors, and researchers in general). We therefore consider
the Centre to be well positioned and prepared to meet the requirements
of a PhD-school (or Researcher school) as newly proposed by the
Research Council. Anyway, we plan to educate a significant number
of new researchers.
The main goals of the research activity for the next ten years
can be summarized as
To create a national research centre with an atmosphere where
the participants continue to do first rate research in geometry,
stochastic analysis, differential equations, and applications
in physical sciences.
To arrange a "kick-off" conference in 2003 and a
"follow-up" conference two to three years later which
will focus on the interdisciplinary aspects of our research activity.
To create interdisciplinary research activities where we focus
on the interplay between
i) computational geometry and algebraic/differential geometry
ii) computational geometry and differential equations
iii) stochastic analysis and differential equations
iv) stochastic analysis and physical sciences
v) differential equations and physical sciences.
As a national centre in applied mathematics our intention is
to cooperate with a variety of research groups in Norway which
are in need of such expertise. The cooperation with SINTEF Applied
mathematics will provide the centre with an open channel to industrial
problems. If our capacity permits, the centre may also be involved
in other joint projects, for example in basic petroleum research
A major purpose of the centre will be the training of new researchers.
Our expectations is that approximately 25 Ph.D. candidates associated
the centre will graduate during the ten year period, with approximately
ten completing their degree during the first five years. Similar
figures exist for the estimated number of Post.docs. (These estimates
also includes a few candidates who work with some of the participants
of the centre as advisors, and therefore will be associated the
centre when it starts to operate, but have begun their Ph.D. studies
before the centre existed.)
In the following sections, we present the four main projects with
its main goals.