27 November – Mario Kummer: Fourier Quasicrystals
Quasicrystals were discovered in the 1980s and have led to a paradigm change in crystallography. Their existence shows that order can exist without regular repetition. They scatter X-rays into patterns with sharp peaks, much like ordinary crystals. Yet the mathematics behind this picture holds a surprise: in many models, countless faint peaks fill the gaps and remain hidden only because instruments cannot detect them. Can we find patterns whose diffraction peaks are truly isolated, even when no signal is too faint to detect? This talk introduces these objects, known as Fourier quasicrystals, and the search for examples that do not repeat periodically. Their construction draws on an unexpected source: algebraic geometry. In fact, there is a natural correspondence between Fourier quasicrystals and certain algbebraic subvarieties of the algebraic torus. This is based on joint work with Lior Alon, Pavel Kurasov, and Cynthia Vinzant.
Mario Kummer is professor for real algebraic geometry at TU Dresden, where he has worked since 2020. He earned his doctorate at the University of Konstanz in 2016 under the supervision of Claus Scheiderer. Before going to Dresden, he was a postdoc at the Max Planck Institute for Mathematics in the Sciences in Leipzig and a junior professor at TU Berlin. His research explores real algebraic geometry and its connections to combinatorics, optimization, and the mathematics of quasicrystals.
