The group in Computational Mathematics does mathematical research in geometrical modeling, partial differential equations, numerical analysis, combinatorics and optimisation. Much of the activity is motivated by applications, and very central is the development of numerical algorithms and their analysis.
The mathematical foundation of our research lies within analysis, linear algebra, differential equations and optimisation, including a computational approach.
Partial differential equations (PDEs) are used in a wide range of applications like weather and climate models, molecular biology and ecology, and removing noise from digital images. For instance, a PDE may describe how the temperature of an object will develop during time when its boundary is heated up. The group works on the mathematical analysis of PDEs, as well as the development and analysis of numerical methods for approximating solutions to these equations. A central topic is to understand the properties of these approximation methods, such as its stability and convergence.
In geometrical modeling one works with problems related to digital geometrical models. Such models are used in industrial design, animation, computer games and other areas. Splines are functions defined via polynomials and they are very important in order to represent geometrical objects and functions in a flexible and efficient way.
Mathematical optimisation is an important part of applied mathematics where one studies min- and max-problems. Many interesting problems lie at the borderline of optimisation and combinatorics; there are lots of applications, and nice mathematics like polyhedral theory and combinatorial matrix theory. Several problems in industrial engineering, mathematical finance and economics may be studied and solved using optimisation.
The CM group currently has 6 permanent faculty positions and a number of PhD students, postdocs and visitors.