A new look at dynamical systems

Associate Professor Magnus Goffeng 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.

An effective way of describing the world around us is by using dynamical systems. They deal with events that change over time – everything from the weather to financial markets. However, the world is complex and events are often chaotic. To better understand their intricate behaviour and predict future development, this project will make use of a powerful and original mathematical framework: non-commutative geometry.

Non-commutative geometry merges the analytical techniques of quantum mechanics with geometric concepts from the general theory of relativity. For example, it challenges the idea that multiplying functions always gives the same result regardless of the order in which it occurs. A common feature of non-commutative geometry is that classical concepts such as geometry, space and coordinates take on a new meaning.

Therefore, a new set of tools will be created to analyze dynamical systems by treating important observable quantities such as position and momentum as non-commutative operators. This approach reveals the hidden symmetries and structures within the system, making new behaviors visible and advancing the understanding of global properties of dynamical systems. By reshaping geometry and mathematical operations, the project digs deep into complex systems, revealing hidden order within apparent chaos. This paves the way for groundbreaking discoveries in vast areas, from science and technology to all others where changing processes in our world are studied.