Geometric Analysis and Mathematical Physics

Geometric Analysis and Mathematical Physics is a Centre of Excellence nominated by the Academy of Finland for the years 2002-2007. It combines top-level Finnish research on geometric analysis, which has a long tradition in Finland, and on mathematical physics, which is a relatively new and rapidly expanding area in Finnish mathematics.

Collaboration

This centre is also a joint venture between the Department of Mathematics and Statistics of the University of Jyväskylä and Department of Mathematics of the University of Helsinki. The centre carries on the collaboration of the mathematical analysis groups in Helsinki and Jyväskylä whose roots go back to the foundation of the Faculty of Mathematics and Natural Sciences of the University of Jyväskylä in 1965. The emphasis in this collaboration has been geometric analysis and its most central research areas are quasiconformal mappings, which has for a long time been the strong area of Finnish mathematics, its generalizations and related nonlinear partial differential equations and potential theory.

The collaboration between the mathematical physics group of Helsinki and the geometric analysis group is a novel feature of Finnish research in mathematical analysis.

Research interests

The research of the geometric analysis group in Jyväskylä is quite wide-ranging. Quasiconformal mappings still have a central place, and they have been applied to material science. Their generalizations, mappings of finite distortion, are inherent in elasticity theory. Analysis in metric spaces has been developed in many different aspects. In nonlinear partial differential equations and potential theory, research has been directed to uniqueness and regularity properties for equations with irregular data and viscosity solutions. Methods of geometric measure theory have been used to study complicated fractal type objects. In mathematical physics, we investigate chaotic and complicated phenomena. One of the most central of these is the turbulence of liquid and gas flows.