Exploring the uncertainty principle in new contexts

Alex Bergman will receive his doctoral degree in mathematics from Lund University in 2026. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will hold a postdoctoral position with Professor Aleksandr Logunov at the Massachusetts Institute of Technology, Cambridge, USA.

Alex Bergman will receive his doctoral degree in mathematics from Lund University in 2026. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will hold a postdoctoral position with Professor Aleksandr Logunov at the Massachusetts Institute of Technology, Cambridge, USA.

The planned project addresses two topics related to the uncertainty principle of quantum physics. This principle has also reached a wider audience through the famous thought experiment known as Schrödinger’s cat, in which a cat trapped in a box can be considered as both alive and dead at the same time. The cat illustrates one of the most fundamental insights of quantum mechanics, formulated nearly a century ago by German physicist Werner Heisenberg: it is impossible to assign exact simultaneous values to the position and momentum of a physical system.

Since then, the study of the uncertainty principle has become a central element of harmonic analysis, the branch of mathematics that investigates how complex objects and signals can be represented and constructed using a limited number of simple building blocks. Harmonic analysis has a very broad range of applications, and is used in areas such as data storage, medical signal processing, X-ray technology, artificial intelligence and telecommunications.

The aim of the project is to investigate the uncertainty principle in non-linear systems – systems that depend on many parameters – and in curved geometries. Curved geometry comprises the mathematical basis for general relativity theory, while non-linear systems can describe phenomena such as weather, economic models and electronic components such as transistors. Over the past twenty-five years, several new and powerful methods have been developed in these areas of mathematics, which means that answers to many exciting and important questions – ones considered too difficult to answer at the turn of the last millennium – are now within reach.

Photo: Unknown