Jens Wittsten received his Ph.D. in mathematics at Lund University in 2010. He will hold a visiting research position in Professor Setsuro Fujiie’s group at Ritsumeikan University in Kyoto, Japan.
Jens Wittsten’s area of expertise, microlocal analysis, has been developed in order to study solutions of partial differential equations. Its techniques have many applications.
For example, the theory has been used to study the accuracy of the representation of earth’s interior based on earthquake data. The description cannot be complete because the problem is too complex and the equations used to describe it are non-linear and therefore difficult to analyze. In addition, there is not enough data from the measurements. One tries to find the best interpolation methods in order to get the best possible image.
New developments show that the theory can be applied also to dynamical systems, i.e. mathematical models of phenomena which evolve with time, like fluctuations of stock prices, or movements of particles in gas. So far microlocal analysis has been applied only to chaotic systems where noise is absent. The extension of the theory allowing for the presence of noise is the next step. Noise can cause large divergence in the evolution of a chaotic system.
The goal of the project is to find properties of the model, which are robust with respect to noise. Professor Fujiie and his group have expertise in this field and collaboration with them can prove to be very productive.