DOCTORAL SCHOOL: MATHEMATICS AND PHYSICS

1. ACADEMIC PROFILE

Research education in science at Aalborg University is possible in mathematics and physics. The programme involves:

• The Department of Mathematical Sciences
• The Department of Physics and Nanotechnology.

Research in mathematics is currently grouped under three headings:

• Applied mathematical analysis
• Discrete mathematics
• Probability and statistics

The Department of Mathematical Sciences is focusing its research in fields of particular relevance for technical and computing applications. (See Section 2 below).

Research in physics is currently grouped under the following headings:

• Nano optics
• Theoretical studies of nanostructures
• Experimental studies of nanostructures
• Surface and interface physics

As these headings indicate the Department of Physics and Nanotechnology has strong focus on aspects of physics related to structures with nanoscale dimensions.

2. RESEARCH FIELDS

Education to the level of PhD is normally attached to a field where active research is performed at Aalborg University, but education within other subjects in mathematics or physics can be arranged in co-operation with other institutions in Denmark and abroad.

Applied mathematical analysis:

This field is concerned with problems having their origin in physics or the engineering sciences, and involving mathematical analysis. This covers the development and study of mathematical concepts used in the formulation of physical theories, or engineering modelling, as well as mathematical methods used in the solution of particular problems that have been formulated, for example, by differential equations. At Aalborg University the research currently evolves around problems in mathematical quantum mechanics with application in nanophysics, applied harmonic analysis with applications in signal processing, non-linear and inverse boundary value problems, and inverse problems for partial differential equations.

Contact person: Arne Jensen, Professor.

Discrete mathematics:

Several sub-disciplines are covered under this heading. A common characteristic is the application of combinatorial arguments and an interest for incidence structures, typically described using linear algebra. At Aalborg University there is research activity in graph theory and combinatorics, coding theory, and information theory.

Contact person: Lars Døvling Andersen, Professor.

Probability and statistics:

This area is concerned with interpretation and analysis of scientific and practical problems using data that have been collected in observational or experimental studies. Research in statistics range from very mathematical or philosophical aspects to practical and computational aspects, in a natural interaction with other fields. At Aalborg University, research activities are mainly concerned with complex stochastic systems, in particular the theoretical and computational aspects of models for spatial variation and dynamic models, with applications in agricultural and medical research. Research on stochastic networks, with application in wireless communication, and bio and forensic statistics play an important role as well.

Contact person: Jesper Møller, Professor.

Nano optics:

Miniaturizing optical components and controlling optical processes at the subwavelength scale are strategic initiatives for both information and sensor nanotechnologies. Optical components involving surface plasmons sustained by nanostructures exhibit excellent radiation confinement and giant field enhancements, which are very attractive features opening a doorway to abundant industrial applications. The primary experimental techniques are linear and non-linear optical microscopy and scanning near-field optical microscopy.

Contact person: Sergey Bozhevolnyi, Professor.

Theoretical studies of nanostructures

Metallic, semiconducting and organic nanostructures are studied using quantum mechanical and statistical tools. In particular, metallic quantum wells, carbon nanotubes as well as organic and inorganic nanowires are studied. The focus is on optical and electronic properties of such nanostructures. There is close collaboration with experimental groups for characterization and synthesis of nanostructures. The quantum mechanical tools range from semi-empirical ones to density-functional theory. The studies range from fundamental work to nanostructures applied in sensors and light-emitting diodes.  

Contact person: Thomas G. Pedersen, Associate Professor

Experimental studies of nanostructures:

Nanostructures in the form of thin films, wires, and dots are interesting building blocks for future electronic and optical components. Semiconductor nanowires, carbon nanotubes, and ultra-thin films are synthesised and characterized. The focus is on linear and non-linear optical properties of these low-dimensional systems as well as devices for electronic, optical and sensor technology. 

Contact person: Kjeld Pedersen, Associate Professor.

Experimental surface and interface physics

The electronic and geometrical structures of interfaces and surfaces are studied. Adsorption and reactions on modified surfaces are investigated by means of a series of spectroscopies. The geometrical characterization of the low-dimensional systems includes scanning probe microscopies. Bimetallic surface alloy systems are created under well-controlled conditions and their reactivity is measured. The experimental information on the bimetallic bond and the structure of the alloys, in 2- and 3-dimensions, are compared with theoretical predictions. Self-assembled monolayers involving organic materials are produced and characterized by scanning tunnelling microscopy.

Contact person: Jens Onsgaard, Professor.

3. COURSE ACTIVITIES

The research education in science includes course work. Some courses have as their main purpose to broaden the general background knowledge of the PhD students, and some the purpose of studying subjects of specific relevance to the PhD projects. Note that several of the courses are of interest to PhD students in engineering sciences.

Courses are arranged periodically and can be held as lectures, reading classes, seminar courses or self-study, as it appears feasible.

Examples of such courses are:

Advanced graph theory

This course introduces PhD students to advanced topics in graph theoretic research, such as the study of structural changes of graphs under edge removal or extremal graph theory.

Information theory

The course covers fundamental theories and methods from information theory: Entropy and datacompression codes, channel capacity and errorcorrecting codes, application of information theoretic methods in statistics.

Design and analysis of experiments

The course covers factoral designs and design methods for response surface analysis.

Stochastic simulation and examples of applications

This course covers the theory and application of pseudorandom number generation as a tool for the study of complex stochastic systems. Markov chain Monte Carlo methods and other methods of simulation are studied.

Harmonic analysis and differential equations

The course introduces the PhD students to advanced functional analytic methods in applied mathematical analysis such as the theory of distributions, Sobolev spaces and pseudodifferential operators.

Introduction to wavelets

Wavelets are an important and very flexible mathematical tool in analyzing and synthesizing signals and images. The course is an introduction to this area of research.

Numerical methods

The course covers basic topics in numerical analysis, including the basics of floating point computations, numerical linear algebra, and the finite element method.

Quantum theory of atoms and condensed matter

The course aims at giving the PhD students a solid introduction to those parts of quantum mechanics which play a crucial role for the understanding of the electrodynamical (optical) properties of atoms and condensed media, e.g. solid surfaces and bulk matter.

Optical properties of atoms and condensed matter

Based on a quantum physical description, the course aims at giving the students a basic and general insight in the linear and non-linear optical properties of atoms, surfaces and bulk matter.

Near-field optics

The course seeks to give an introduction to near-field optics, i.e. light-particle interaction on a subwavelength scale. Both theoretical and experimental aspects are covered.

Solid surfaces, and interfaces and thin films

The course covers experimental and theoretical topics in the physics and chemistry of surfaces, interfaces and thin films, including aspects of nanomaterials. Both the preparation and the characterization of low-dimensional structures are treated. Their geometrical and electronic structures are studied. Adsorption and growth phenomena are introduced.

Courses held in the final years of the M.Sc. programme in mathematics can be merited as research courses in mathematics, provided they have not already been merited for the M.Sc. degree.

Courses at other institutions in Denmark and abroad can be merited as research courses upon application.

4. PHD STUDENTS AND SCIENTIFIC PERSONNEL

The current statistics for PhD students and degrees awarded is given below (note that PhD study in “mathematics education” is currently not offered by the Department of Mathematical Sciences):

	Completed	Under study
Applied mathematical analysis	10	1
Discrete mathematics	5	1
Probability and statistics	23	2
Mathematics education	2	0
Theoretical physics	8	2
Experimental physics	8	5

 
The scientific staff at the Department of Mathematics at Aalborg University currently totals 29 full-time professors, associate professors and assistant professors, and a number of associated researchers. The Department of Physics and Nanotechnology has a full-time staff of 13 professors, associate professors and assistant professors, and a number of associated researchers.

5. EXTERNAL CO-OPERATION

All groups mentioned have a well developed national and international research co-operation with mathematics and physics groups all over the world. This involves a regular stream of mutual visits and exchange of information, as well as direct research co-operation. The international mathematics and physics environments form indeed very dense networks, and staff members at Aalborg University are participating at full rate. Research co-operation in mathematics does also involve participation in cross-disciplinary activities within Aalborg University.

International research partners in mathematics include:

• University of Chicago and University of Missouri (USA)
• University of Montreal (Canada)
• Cambridge University Oxford University University of Lancaster, and City University (England)
• University of Perth (Australia)
• University of Tokyo and Nagoya University (Japan)
• Hungarian Academy of Sciences
• Rumanian Academy of Sciences
• INRIA and CPT Marseille (France)
• Ecole Polytechnique Federale Lausanne (Switzerland)

The Department of Physics and Nanotechnology has research co-operation with:

Laboratoire d'Electromagnetisme, Microondes et Optoelectronique, Grenoble(France).
• Institute of Spectroscopy, Russian Academy of Sciences, Troitsk and International Laser Center, Moscow State University (Russia).
• Departemento de Fisica de la Materia Condensada, Madrid (Spain).
• Laboratoire de Sciences et Ingénierie des Surfaces, Lyon (France).
• Dept.of Theoretical Physics, University of Paderborn (Germany).
• ISIS, Université Louis Pasteur, Strasbourg (France)
• Institute of Physics, Karl-Franzens University, Graz (Austria)

Co-operation in Research Education:

Under the heading DINA (Danish Informatics Network in the Agricultural Sciences) Postgraduate School there is a co-operation between institutions in agricultural research and informatics (including mathematics and statistics) in Denmark with the purpose of introducing PhD students in agricultural research to informatics and vice versa. Within the subject of probabilistic expert systems there has been formal co-operation about research education between the fields of computer science and engineering, environmental engineering, and mathematics.

Whenever practicable, research students have spent shorter or longer periods at universities abroad. The list of institutions who previously have hosted PhD students from the Department of Mathematics include:

• University of Hawaii, University of Washington, University of South Carolina, and Berkeley, University of California (USA)
• University of Surrey, University of Cambridge, and University of Lancaster (UK)
• Centrum voor Wiskunde en Informatica and Technical University of Eindhoven (Holland)
• Paris Université VII (France)
• KTH, Stockholm (Sweden)

The list of institutions that previously have hosted PhD students from the Department of Physics and Nanotechnology include:

• University of Toronto (Canada).
University of California at Berkeley (USA).
• Indiana University, Bloomington (USA).
• University of Nijmegen (Holland).
• Osaka University (Japan).
• IBM Zürich (Switzerland).
• University of Paderborn (Germany)

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Information updated December 2, 2005

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For further information, please contact
Professor Jesper Møller
Department of Mathematics
Institute of Mathematical Sciences
Fredrik Bajers Vej 7G
DK-9220 Aalborg East
Telephone +45 9635 8863
E-mail jm@math.aau.dk

 

Revised: 04.20.2007