The Department of Physics and Mathematics has operated in Joensuu since 1970. We educate teachers of physics and mathematics, mathematicians, and physicists who specialise in photonics. In photonics, we also offer an international Master’s degree programme. Our education is based on internationally acclaimed, top level scientific research.

We also participate in the Finnish Flagship on Photonics Research and Innovation (PREIN), funded by the Academy of Finland, which focuses on light-based technologies and their various applications, as well as the social impact of photonics.

We have world-class laboratories that enable the development of nanotechnology-based experimental photonics and support the department’s solid theoretical research. Our laboratories are also used for teaching purposes, and we offer laboratory services to research partners and companies outside the university as well.

## 85

### Experts and professionals

## 47

### Bachelor's degree awarded per year

## 43

### Master's degree awarded per year

## Studies

The major subject choices for the degree programmes offered at our department are mathematics, physics and chemistry, and the subject teacher training programme also gives the opportunity to specialise in computing. The major subject is chosen during the first year of degree studies, but it is easy to change between major subjects or degree programmes within the department also later during the studies. Specialising in photonics is also possible in an international Master’s degree programme, usually after completing a Bachelor’s degree in physics.

Physicists and mathematicians who graduate from our department find employment in research and experts positions in higher education institutions, research institutes, and companies, while subject teachers in physics and mathematics find careers in secondary and upper secondary schools.

## Bachelor's and Master's degree programmes (in Finnish)

## International Master's degree programmes

## Research

Our areas of research are photonics, mathematics, and research on physics and mathematics education. The quality of our photonics and mathematics research meets the standards of excellence internationally. Our Center for Photonics Sciences is a network that brings together all photonics research at the university. The multidisciplinary institute has a unique collection of photonics professionals and is a world-class research environment.

Photonics is an important research area at the University of Eastern Finland. A research community adhering to the university’s strategy for the future has been formed around photonics, which also includes the medical research carried out at the A.I. Virtanen Institute for Molecular Science.

Participating in the Finnish Flagship on Photonics Research and Innovation (PREIN) are Tampere University, Aalto University, and VTT Technical Research Centre of Finland.

The focus areas in mathematics research are complex analysis and partial differential equations.

## Research areas

In photonics one investigates light, its properties, and its utilization in various applications in, e.g., ICT and medical sciences. Photonics research and education at UEF is under the Center for Photonics Research.

Complex Analysis, or Complex Function Theory, is a field of mathematics which studies analytic or meromorphic functions, integration and mappings in the complex plane or its subsets.

**Value Distribution Theory**

Nevanlinna theory (or value distribution theory) deals with the growth and value distribution of meromorphic functions. One of its central results is the second main theorem, which is a deep generalization and quantification of Picard's theorem. The basic theoretical structure analogous to Nevanlinna theory can be found in many areas of mathematics such as *p*-adic function theory, minimal surfaces and even Brownian motion. According to the work of Osgood and Vojta the second main theorem of Nevanlinna theory corresponds to the ABC conjecture in number theory, which in turn implies asymptotic version of Fermat's Last Theorem. Another interesting analogue is the so-called Tropical Nevanlinna theory discovered by Halburd and Southall, which deals with piecewise linear real functions over a max-plus semiring. Applications of Nevanlinna theory can be found mostly in other branches of mathematics, such as complex oscillation differential and functional equations, or in areas adjacent to mathematics, such as mathematical physics.

**Operator Theory and Function Spaces**

Research on operator theory concentrates on concrete operators such as the Bergman projection, Toeplitz, Hilbert, integral and composition operators acting on spaces of analytic functions in the unit disc employing harmonic and functional analysis. In function spaces the main focus lies on small Bergman spaces whose harmonic analysis is somewhat similar to that of the Hardy spaces and is therefore challenging compared to the case of standard Bergman spaces.

**Differential Equations**

The long development of theory of linear differential equations in the complex domain has created an extensive network of international collaboration. One of the starting points has been the study of growth of solutions in case of the complex plane, from which researchers have proceeded to consider similar problems in the unit disc. The Joensuu research group has been particularly strong in applying the theory of analytic function spaces in differential equations.

Another central theme of recent research activity has been the oscillation theory. For example, in case of the unit disc the study of oscillation of solutions is an interesting combination of value distribution theory of meromorphic functions, function spaces, univalent functions, interpolation and non-Euclidean geometry. One of the main objectives is to describe the geometric zero distribution of solutions.

After some quiet years the research on complex differential equations in the case of plane has started a new rise. The subjects of research are now special solutions in terms of canonical products and contour integrals, and the oscillation of solutions in the case when the coefficient functions are exponential polynomials, to name a few. Moreover, cases in which the coefficient functions are special functions have recently attracted interest.

The contact information of Complex Analysis research group you can find from UEF Connect.

The research on partial differential equations can be divided into two subtopics: overdetermined problems and their numerical solution, and nonlinear potential theory.

Overdetermined problems occur both in pure and applied mathematics. The framework for analyzing such systems, the formal theory of partial differential equations, is based on considering a given equation as a submanifold in a suitable jet space. We have shown that the central concept of the theory, the involutive system, is also useful in the numerical solution of partial differential equations. This research is done in collaboration with Bijan Mohammadi (Université de Montpellier).

The algebraic tools which are also useful in the formal theory has also lead to the analysis of some constrained systems in multibody dynamics. Here the focus is on the analysis and characterization of possible singularities of the configuration space of the multibody system. This topic is studied in collaboration with Samuli Piipponen (University of Tampere) and Andreas Müller (Johannes Kepler Universität Linz).

The research on nonlinear potential theory concentrates on the regularity theory of solutions and supersolutions of nonlinear elliptic problems in metric spaces and in variable exponent spaces. In particular, the potential theoretic problems related to the fine topology are studied. The research related to the variable exponent is a part of the national research network Finnish variable exponent Sobolev spaces research group. The research on metric spaces is based on the co-operation with Anders and Jana Björn (Linköping University) and Tomasz Adamowicz (Institute of Mathematics, Polish Academy of Sciences).

Research on teaching and learning of physics and mathematics is based on the traditions of Physics Education Research (PER) and Mathematics Education Research. The research produces detailed knowledge about the factors influencing student learning. The results are used as a base in developing novel solutions for teacher education in mathematics and physics and for school teaching as well.

The most salient themes related to teacher education are teacher knowledge of mathematics and physics teachers and students’ mathematical-related orientations. Mathematics in engineering education is studied in cooperation with Karelia University of Applied Sciences. The projects belonging to the LUMA FINLAND programme focus on two themes: 1) the integration of technology education in physics and chemistry teaching at school, and 2) reducing the effects of sex segregation in students’ education and career choices in science and engineering fields.

**Contact person:**

- physics or mathematics education research or doctoral education: Asikainen Mervi, Senior Lecturer
- issues related to LUMA: Risto Leinonen, postdoctoral researcher

The contact information of Physics and Mathematics Education research group you can find from UEF Connect.

## Our research groups and projects

## News and Events

### News

## Contact information

University of Eastern Finland’s Student and Learning Services is responsible for providing general study-related administrative services for students and staff, as well as offer support for applicants.

Read more: Student and Learning Services

**Postal address**

University of Eastern Finland

Department of Physics and Mathematics

Joensuu Campus

P.O. Box 111

FI-80101 JOENSUU

**Street address**

Yliopistokatu 7

Metria building