Abstract Methods in Mathematical Physics

Mattias Jonsson is at present Professor of Mathematics at the University of Michigan, Ann Arbor, USA. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will be Visiting Professor at the Department of Mathematical Science, Chalmers University of Technology and the University of Gothenburg.

Solutions of polynomial equations can be visualized geometrically. Algebraic geometry is the branch of mathematics which studies such geometric objects. They are called algebraic varieties. Mattias Jonsson will join a group of mathematicians in Gothenburg who apply methods of mathematical analysis to study complex algebraic varieties. Their research is in part motivated by questions arising from Einstein’s relativity theory. It is also closely related to studies of an important conjecture of Yau-Tian-Donaldson.

Mattias Jonsson is an expert in the area on the border between mathematical analysis and algebraic geometry, non-Archimedean geometry, which has been developed by mathematicians over the last half century. It replaces the familiar real and complex numbers with other abstract constructs called non-Archimedean fields.

There exist some indications that methods of non-Archimedean geometry may prove successful in taking steps towards proving some of the most central parts of the complex geometry which are closely related to the theory of relativity. Especially big expectations are tied to combining methods of non-Archimedean geometry and complex analysis in order to manage the famous Kontsevich-Soibelman conjecture, motivated by the string theory of theoretical physics.

Photo: University of Michigan