International Exchange of Ideas and Results
The numerical range plays a crucial role in spectral theory and in the search of ground-state energies of quantum physical systems. In 1918/1919, by the celebrated Toeplitz-Hausdorff theorem, it was shown to form a convex set.
In quantum-many-body systems – the focus of interest in the International Doctorate Program „Exploring Quantum Matter“ – the important question arises whether the spectra of the underlying Hamiltonians are gapped. This decision problem was brought to Gödel-form by Prof. Michael Wolf (who is an ExQM PI) in a seminal paper in Nature. His talk on “Undecidability of the Spectral Gap” was one highlight of the conference.
First-year ExQM PhD student Frederik vom Ende presented his results on infinite-dimensional systems and found himself immediately well received in the community.
Upon invitation by ExQM, Prof. David Gross (University of Cologne) lectured on low-rank reconstruction algorithms. They are important not only in quantum physics but also in every-day-life when it comes to image reconstruction and signal processing.
Mathematicians in Germany 1933-45, a Cultural Round-Up
Prof. Thomas Huckle (who also is an ExQM PI) gave an overview on the fate of mathematicians in Germany 1933-45 (including the celebrated Hausdorff and Toeplitz) with special hints to the then running exhibition “Die Technische Hochschule im Nationalsozialismus”. – An excursion to the collection of the Blue Rider in Lehnbachhaus was a cultural round-up.
Text: International Doctorate Program "Exploring Quantum Matter“