SCHOOL: MATHEMATICS AND PHYSICS
1. ACADEMIC PROFILE
Research education in science at Aalborg University
is possible in mathematics
and physics. The programme involves:
Research in mathematics is currently grouped under three headings:
Department of Mathematical Sciences is focusing its
research in fields of particular relevance for technical
and computing applications.
Section 2 below).
Research in physics is currently
grouped under the following headings:
- Nano optics
- Theoretical studies of nanostructures
- Experimental studies of nanostructures
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
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.
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
Contact person: Arne Jensen,
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
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
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
on stochastic networks, with application in wireless
communication, and bio and forensic statistics play an
important role as well.
Contact person: Jesper Møller,
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
Theoretical studies of
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
Experimental studies of
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.
person: Kjeld Pedersen, Associate Professor.
Experimental surface and interface physics
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
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
Contact person: Jens
3. COURSE ACTIVITIES
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
Advanced graph theory
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
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
course covers factoral designs and design methods for
response surface analysis.
Stochastic simulation and examples
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
Harmonic analysis and differential
course introduces the PhD students to advanced functional
analytic methods in applied mathematical analysis such as
the theory of distributions, Sobolev spaces and
Introduction to 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.
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
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
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.
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.
surfaces, and interfaces and thin films
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
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.
at other institutions in
Denmark and abroad can be merited as research courses upon
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):
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
International research partners in
University of Chicago and University of Missouri (USA)
University of Montreal (Canada)
- Cambridge University
University of Lancaster, and City University (England)
of Perth (Australia)
University of Tokyo and Nagoya University
- INRIA and CPT Marseille
- Ecole Polytechnique Federale
Department of Physics and Nanotechnology has research
Laboratoire d'Electromagnetisme, Microondes et
Institute of Spectroscopy, Russian Academy of Sciences, Troitsk and International
Laser Center, Moscow State University (Russia).
- Departemento de Fisica de la Materia Condensada,
- Laboratoire de Sciences et Ingénierie des
Surfaces, Lyon (France).
Theoretical Physics, University of Paderborn (Germany).
- ISIS, Université Louis
Institute of Physics, Karl-Franzens University, Graz
in Research Education:
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.
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:
of Cambridge, and University of Lancaster (UK)
voor Wiskunde en Informatica and Technical University
of Eindhoven (Holland)
Paris Université VII (France)
of Hawaii, University of Washington, University of
South Carolina, and Berkeley, University of California
list of institutions that previously have hosted PhD
students from the Department of Physics and Nanotechnology
of Toronto (Canada).
University of California at Berkeley (USA).
University, Bloomington (USA).
- University of Nijmegen (Holland).
- University of Paderborn
updated December 2, 2005
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