The purpose of the programme

In our time, mathematics plays a crucial role in other fields of  science and practice as well as in technology, planning and the control  of systems and processes of societal significance. This role is brought  about predominantly through the building, employment and assessment of  mathematical models on the basis of existing mathematics or mathematics  developed ad hoc.

Against this background, the aim of the present PhD programme is to  educate PhDs with competencies to create, analyse and utilise  mathematical models in extra-mathematical fields such as biology, medicine,  chemistry, economics, physics and planning, as well as PhDs  with competencies to create, analyse and utilise  mathematical tools of  actual or potential use in mathematical modelling.

This constitutes a dual perspective on a continuum of activities,  ranging from the building and utilisation of concrete models, over  fundamental investigations of mathematical and other prerequisites and  conditions of models and their properties, to historical or  philosophical studies of this interplay. In this way, mathematical
modelling has direct access to a wide range of fundamental mathematical  activity, which, in turn, receives inspiration for the development and  analysis of new mathematical results and tools stimulated by modelling activities.

The objective of the PhD programme is to train students with a Master degree in mathematics or a similar subject to become researchers in a  field of mathematical modelling and its mathematical prerequisites.  This objective is reached through individual research projects and  participation in a number of relevant courses, seminars and conferences.

Main research areas

This programme (which is unique in Denmark) draws upon the dynamic  environment of mutually fertilising expertise within relevant fields,  which has been established at IMFUFA over several decades. Faculty members associated with the programme are at the front end of  development within their respective sub-fields, both by virtue of the significant research contributions they have made and by virtue of  their record as long-standing pioneers, in particular as supervisors of  a large number of master's and PhD projects pertaining to it. Thus,  this programme benefits greatly from the wide and multi-faceted  international and national networks. Examples of institutions with which there is particularly close contact are listed below. Finally,  the scientific environment surrounding the programme is characterised
by extensive collaboration between the mathematicians and the  physicists in the department, especially as regards modelling problems  and issues.

As examples of research pertaining to the programme, which has been conducted at the department so far, the following can be mentioned:

• Modelling of the human blood flow, including mechanisms of  cardiovascular control
• Patient specific modelling and parameter estimation
• Modelling auto-immune diseases, such as type 1 diabetes, Morbus Crohn, and Rheumatoid Arthritis
• Modelling melancholic depression and the HPA-axis
• Modelling of the dynamics of populations, in particular the development and dissemination of infectious diseases
• Partial differential equations and their role in the modelling of  physical and biological systems
• Real and complex dynamical systems, including holomorphous dynamics  and the study of fractal structures
• Statistical and mathematics methods for the description of  vegetation spread and growth
• Optimisation and control of systems and processes
• Historical and philosophical studies of the relations between mathematical optimisation and the development of its mathematical  foundation

Organisation and content of the programme

The emphasis of this PhD programme is on the individual PhD students writing of a dissertation. For each student admitted to the programme,  an individual plan of study is established in close collaboration between the student and his/her supervisor. Normally, work oriented  specifically towards the writing of the dissertation is expected to take up at least two of the three years of study. The progress and plan  of study is subjected to critical scrutiny and modification at regular intervals by the student and his/her supervisor. The study plan should  indicate ways in which the student can be integrated as an active member of the research environment in the Department, and ways in which the student can be brought into contact with other Danish or international research centres in his/her field of interest. The continuous revision of the study plan will also address which specific  PhD courses, research symposia and other conferences the student ought  to take part in or contribute to.

Admission to the programme

Admission to the programme requires a university degree at masters  level in mathematics or similar subjects. However, students with a different background may be admitted to the programme as circumstances indicate. In all cases, a student applying for admission is requested  to sketch his/her research interests by providing a brief preliminary  outline of a research project.  The programme typically addresses graduates who, in addition to having demonstrated independent  scientific and scholarly ability, have a genuine interest in  mathematics.

Participating departments at Roskilde University

 Department of Studies in Mathematics and Physics and their Functions in  Education, Research and Applications

Participating institutions outside Roskilde University

The Mathematical Modelling research programme and its mathematical prerequisites is associated with the national PhD programme called  'Forskerskole i matematik og anvendelser' (Research School for  Mathematics and Applications) and its collaboration with other  universities and research institutions in Denmark, such as the
University of Copenhagen, Aarhus University, and the Technical  University of Denmark.

Foreign research institutions with which the associates of the programme have established particularly close working relations, and at  which PhD students under the programme will be welcome visitors, are:

Caltech, Pasadena, USA
University of Cambridge, UK
University of Cergy-Pontoise, France
Cornell University, Ithaca, NY, USA
Simon Fraser University, Vancouver, Canada
University of Graz, Austria
Harvard Medical School, Cambridge, MA, USA
Kungliga Tekniska Högskolan, Stockholm, Sverige
University of Mainz, Germany
Max-Planck-Institut für Mathematik, Bonn, Germany
State University of New York at Stony Brook, NY, USA
North Carolina State University, Raleight, NC, USA
University of Paris XI (Centre Universitaire d'Orsay), France
University of Pennsylvania, Philadelphia, PA, USA
Princeton University, Princeton, NJ, USA
University of Toronto, Ontario, Canada
University of Trento, Italy

Further information

Professor Johnny T. Ottesen,
Department of Sciences, Systems and Models,
Roskilde University, Building 27,
PO Box 260,
DK-4000 Roskilde
Tel + 45 4674 2298,
Fax + 45 4674 3020,
Email Johnny@ruc.dk