Andreas Rosén will receive funding for a postdoctoral position for international researchers at the Harmonic Analysis and Partial Differential Equations Group at the Department of Mathematical Science, Chalmers University of Technology and the University of Gothenburg.
Beginning with Newton in the 17th century, many mathematical applications start with a system of differential equations. The solutions can, for example, yield a weather forecast for a week-end, describe the flow of traffic, or growth of bacteria in a Petri dish.
Dirac equations, the subject of the proposed research, are a special category of differential equations. The British physicist and Nobel Prize laureate, Paul Dirac, formulated his equations in 1928 in order to obtain the quantum mechanical description of the motion of an electron. Dirac equations have played an important role in pure mathematics in the last fifty years.
In the 1960s, Michael Atiyah and Isadore Singer developed a new way of looking at some differential equations. Instead of looking for solutions, they asked the question about the size of the solution set. Their theory led to significant progress in the underlying mathematics.
The proposed project is going to utilize the developments in mathematics over the last fifty years. The goal is to study Dirac equations by using techniques of harmonic analysis. Harmonic analysis has been developed in order to study differential equations.
Photo Chalmers University of Technology