Mathematics in quantum physics: Angelika Wiegele is currently researching and teaching at the University of Cologne

The mathematician was invited to contribute to the key profile area “Quantum Matter and Materials” at the University of Cologne as a member of the Global Faculty. There, she is working at the interface between mathematics and quantum physics.

“Mathematics is not something that takes place in secret or in seclusion”, says Angelika Wiegele, a professor at the Department of Mathematics. Instead, the invigorating exchange with colleagues is essential for developing new ideas. “If we put our heads together, the result is ultimately far greater than simply the sum of those heads”, she reckons.

Angelika Wiegele is currently part of the Global Faculty at the University of Cologne. This project allows the key profile areas of the University of Cologne to invite academics as visiting scholars for a defined period of time, and these scholars also undertake to contribute to research and teaching. The coordinators invited Angelika Wiegele to contribute to one of the profile areas producing outstanding research work.

In terms of content, she is working on “Quantum Matter and Materials”. But what does mathematics have to do with physics? Wiegele explains: “The quantum state of a particle can be described as a semidefinite optimisation problem. And it is precisely these optimisation problems that are the subject of my research, albeit in a completely different area until now, namely in combinatorial optimisation.” In Cologne, Angelika Wiegele’s daily interactions now mainly involve working with mathematicians and physicists, and she draws the following conclusion: “We can benefit greatly from each other.” Because physics is not offered as a dedicated subject in Klagenfurt, Wiegele’s residency in Cologne presents her with a unique opportunity: “Problems that I have been aware of for a very long time from one angle, I can now see in a completely new context. In quantum mechanics, these problems occur perfectly naturally and constitute an exact description rather than approximations to problems, as is the case, for example, in combinatorial optimisation. In a sense, semidefinite optimisation is the quantum version of linear optimisation.”

Participation in the Global Faculty “Quantum Matter and Materials” at the University of Cologne covers the years 2022 and 2023. Angelika Wiegele is currently in Cologne for two full months. Spending a period abroad involves considerable logistical and bureaucratic effort, but it is well worth it in her eyes. Quizzed about whether mathematics is an international discipline without cultural differences, she states: “In mathematics, as in other natural science and technical subjects, we have an ideal global means of communication in the form of the mathematical language. We rarely have to deal with cultural barriers. The same applies to the degree programmes: The curriculum for a degree in mathematics only varies very slightly across the globe.” The fact that this is also evident in the practical implementation of degree programmes can be seen clearly at the University of Klagenfurt: Here, the Master’s degree programme “Mathematics” – open to international students – has been taught entirely in English since 2018.