Mathematics and Applications

Research areas

Mathematics and applications combines theoretical and applied research in several areas:

• Theoretical research in algebra, astrophysics, geometry and nonlinear dynamics.
• Applied research focusing on population studies in health and modeling of traffic networks, where mathematical modeling is central.

Collaborations and networks

The research is conducted in close collaboration with both social actors and other universities:

• Collaboration partners from the public sector: Region Blekinge, Blekinge County Council and the Swedish Transport Administration.
• Academic collaborations, nationally and internationally: University West, Linköping University, Mälardalen University and Universidade Federal de Santa Catarina in Brazil.

Research project

• Data-driven analysis of travel times.
• Epsilon-strongly graded algebras.
• Hom-associative and non-associative Ore expansions.
• Modeling and optimisation of systems.
• Material dynamics.
• Optimal quantum transport.
• SNAC (Swedish National Study on Ageing and Care) - a national research study.
• Spectral analysis of distant stars.

Noncommutative Riemannian spin geometry from a bundle theoretic point of view

Riemannian spin geometry is an important topic in differential geometry that is mainly based on the theory of principal bundles and deals with objects such as spin structures and Dirac operators. There are numerous applications in mathematical physics, in particular in quantum field theory where spin structures are an important ingredient in the formulation of theories of uncharged fermions. In non-commutative theory, spectral triples provide a natural framework for non-commutative Riemannian spin geometry.

However, unlike in the classical theory, non-commutative manifolds have not yet been incorporated into the axiomatic description of non-commutative Riemannian spin geometry. The aim of this research project is to provide a new perspective on non-commutative Riemannian spin geometry by systematically developing and studying key concepts of Riemannian spin geometry within the framework of non-commutative principal pinches.

Contact person: Stefan Wagner

The algebraic structure of graded algebras

This project falls within the research area of non-commutative algebra. Graded algebras occur naturally in mathematics and for example physics. In this project we aim to achieve a better understanding of the algebraic structure of algebras graded by groups, inverse semigroups, groupoids, etc.

Natural examples of such algebras are matrix algebras, Leavitt path algebras, group rings, groupoid rings, Steinberg algebras, skew group rings, partial skew groupoid rings, and various rings associated with dynamical systems.

Contact person: Johan Öinert

Combinatorial optimisation - for parallel computer systems and for codes

Mathematical problems arise in many contexts. One is when trying to make a parallel computer work as efficiently as possible. If you can solve these mathematical problems, you have very clear limits on how the computer can be built to be as efficient as possible.

The same is true in coding theory. When we send messages between cell phones or in other ways, the signals are subject to interference. If efficient codes are used, the message can still be reconstructed into what was sent. To do this as well as possible, you need to solve some specific mathematical problems.

Contact person: Håkan Lennerstad

Funders

The research is funded by, among others:

• Carl Tryggers Foundation
• The Crafoord Foundation
• Royal Swedish Academy of Sciences
• Swedish Transport Administration
• Swedish Transport Agency

Research in mathematics with applications is mainly conducted at the Department of Mathematics and Natural Sciences.