New Focus on Old Problems

Professor Sandra Pott will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Centre for Mathematical Sciences, Lund university.

Harmonic analysis is a branch of mathematics that was developed at the beginning of the 19th century by French mathematician Joseph Fourier in his study of heat equations. In order to arrive at the solution, he expressed general functions as infinite series of harmonic waves. Such series are known now as Fourier series. Harmonic analysis has found deep applications in many areas of mathematics.

There are many other ways to express functions as infinite series of a set of base functions. For example, one can use wavelets to compress, save, and recreate data. The motivation for using wavelets comes from applications that include electronics and signal processing.

Research on wavelets has had a deep impact on the modern view of classical harmonic analysis. In particular, the simplest wavelets have found important applications. This has led to development of a new research field, dyadic harmonic analysis, in which classical wave functions are replaced by their much simpler analogues. Consequently, problems that just a few years ago were considered impossible to solve are now within reach, and many mathematicians in the field have shifted their research focus.

The international researcher who will now be recruited for a postdoctoral position in Lund is expected to master many of the new tools and therefore play an important role in the research group’s program.