Gauss Lecture by Prof Dr Katrin Wendland (Albert-Ludwigs-Universität Freiburg)

Symmetries appeal to us aesthetically, they are omnipresent in nature and technology, and they can be used to better understand physical phenomena. We are familiar with mirror symmetries from our own reflection, for example; like these, so-called conformal symmetries leave angles unchanged but distort the image. Katrin Wendland explains how to precisely describe, visualise and classify symmetries in mathematics. Conformal field theories offer applications: These are quantum field theories that describe, for example, the phase transition of an ordinary magnet when it is strongly heated. They are compatible with the conformal symmetries, and it is useful and interesting to search for further symmetries in such theories.

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Katrin Wendland is Professor of Mathematics in the Department of Geometry at the University of Freiburg. She conducts research in mathematical physics and investigates connections between conformal field theories and geometry.