The group Computational Mathematics performs mathematical research in geometrical modeling, partial differential equations, numerical analysis, combinatorics and optimization. A lot of the activity is motivated by applications, and very central is the development of numerical
*algorithms* and related theory.

People have for a long time been interested in the properties of geometric shapes. In geometry one is usually interested in terms like distance, angle, area and volume. Topologists study the qualitative properties of geometric space. As the math has evolved, geometry and topology have grown to an active research area with links to physics and many other parts of mathematics.

The origin of Logic is the formal study of human reasoning. As the use of set theory became more frequent in mathematics during the 19th century, applications of logic to the foundation of mathematics became more important. Mathematical logic is partly the investigation of mathematical models for mathematics, and partly the application of mathematical methods to logic. During the 20th century, the investigation of algorithms and computations became an important part of mathematical logic. These days, logic is also a subject with applications outside philosophy and mathematics, e.g. in computer science and linguistics.

Mechanics is the branch of science concerned with classical forces and the effect forces exert on (solid or fluid) physical bodies.

Theoretical and applied fluid mechanics relate to a large variety of topics such as: flow processes in the subsea and offshore industry, blood flows in thin canals and tissue, strong wave impact on wind turbines in the offshore environment, and on ship and offshore platforms, prediction and warning of long tsunamis caused by landslides, submarine slides and seismic motion, extreme ocean waves and invisible underwater interal waves in the ocean, oil- and gas transport in long pipelines and others.

Solid mechanics may be defined as the study of the principles, and the associated mathematics, that describe the behaviour of solid materials and objects when they are subjected to external actions such as forces, temperature changes and applied displacements. The term is sometimes used in a narrow sense to include only solid materials and deformable bodies. However, in our group we adopt a wider definition that includes structural elements and entire structures (such as bridges, ship hulls and offshore platforms, etc.), the study of which is often referred to as structural mechanics.

Operator algebras is a fast expanding area of mathematics with remarkable applications in differential geometry, dynamical systems, statistical mechanics and quantum field theory. It is at the center of new approaches to the Riemann hypothesis and the standard model, and it forms a foundation for quantum information theory.

Partial Differential Equations is a large subject with a history that goes back to Newton and Leibniz. Many mathematical models involve functions that have the property that the value in a point depends on its value in a neighborhood of the point. Dependencies like these can be modeled with partial differential equations. Well-known examples include SchrÃ¶dinger's equation in quantum mechanics, the Navierâ€“Stokes equations in fluid mechanics, and Einstein's equations in general relativity theory.

The central theme of the field is the study of holomorphic functions and mappings, and the relationship between these and the geometry of the underlying space. Complex Dynamics is central to the group. The field is far reaching as one studies problems varying from mathematical analysis to complex/algebraic geometry, topology and complex dynamics.

The research group in
*Statistics and Data Science* is active in many areas of theoretical and applied statistics, including inference for high-dimensional data, survival and event history analysis, model selection and criticism, nonparametrics, hierarchical Bayesian modelling, time- and space-modelling, and general methodological development motivated from applications in public health, genetics, biology, climate science and other fields.

Our research group develops the theory for modelling and managing different forms of risk: economic, financial, insurance, technical, weather and technological. All of energy, finance and insurance industry evolves around risk analysis, in the same way as planning and control of projects and installations (power plants, networks, airplanes).

Modelling and management of risk in renewable energy markets.