Norwegian University of Science and Technology
Institutt for matematiske fag
Area(s) of Expertise
Complex Analysis. Complex Dynamics
John Erik Fornæss is working in mathematical analysis. This is used to calculate descriptions of the real world and to create simplified models. He is specializing in the use of complex numbers in analysis. Complex numbers are sometimes crucial in describing the world, such as for example in electricity or quantum mechanics. Also in string theory which describes the really small pieces of the Universe, one gets into so called Calabi-Yau manifolds which describe the very small extra dimensions of the Universe.
He specializes in the use of complex numbers in analysis and dynamics. Dynamics is concerned with how systems evolve over time. A basic example is the motion of the moon around the earth, given that the earth also revolves around the sun. This leads to equations which can be modelled using complex numbers to describe the position where the moon hits an imagined plane attached to the moon.
These descriptions appear to be chaotic in computer simulations. Similarly complex numbers can be used to model chaotic behaviour in other systems as well as in abstract general models. One of the main research goals is to understand more precisely the appearance of chaos. It turns out that some regions in space are chaotic while other regions are very stable and non chaotic.