The Mathematics Behind the Theory of Everything

Associate Professor Martin Raum will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.

Martin Raum’s research focuses on modular forms and their applications in several branches of mathematics, as well as in the string theory of theoretical physics. Modular forms are mathematical functions that satisfy certain symmetry conditions. First studied about 200 years ago, they have played an important role in number theory and other branches of mathematics. For example, they provided a crucial step in the proof of Fermat’s last theorem, which was posed in 1637 and completed in 1994.

Nowadays, there are a wide variety of modular forms and their generalizations. There are also interesting relationships between them, which are called lifts, for example Maass lifts. In his project, Raum intends to study a modern variant of these, known as skew Maass lifts. Such lifts are now intensively studied using representation theory, and a large part of the inspiration for this research comes from string theory and quantum field theory.

String theory is theoretical physics’ attempt to unify the two most successful achievements of 20th century physics – Einstein’s general theory of relativity and quantum mechanics. But to link these theories together requires completely new and much more advanced mathematics than has been previously used. While Riemann’s geometry could satisfy Einstein’s theory of relativity, a whole new mathematics is now being developed with the hope of realizing physics’ dream of a theory of everything. And, in this new mathematics, modular forms play a central role.

Photo: Johan Bodell / Chalmers