Topological Quantum Nos. in Quasicrystals | Johannes Kellendonk | 15th Int. Conf. on Quasicrystals

In this tutorial - given at Tel Aviv University in June 2023, during the 15th International Conference on Quasicrystals – we explain the mathematical background for the construction of topological quantum numbers in aperiodic crystals. Often, topological quantum numbers are referred to as Chern numbers, as they arose first as Chern numbers of vector bundles, defined by solutions of the Schrödinger equation for periodic crystals. We explain how to define them in a noncommutive way, which is also applicable to aperiodic crystals. We discuss the relevance of topological quantum numbers in quasicrystals. In this context we explain a particular manifestation of the bulk boundary correspondence, which relates the labeling of gaps in the spectrum of a one-dimensional quasiperiodic Hamiltonian to the phason motion. Speaker: Prof. Johannes Kellendonk, University of Lyon. Presenting the speaker: Prof. Ron Lifshitz, Tel Aviv University https://www.icq15.sites.tau.ac.il/ ____________________________________________________________________________________________ This video is part of a playlist. Direct link to the playlist: https://www.youtube.com/playlist?list=PLNiWLB_wsOg6WaZkMTCTmR4v9SjnnXfcy ? ? ? ? ? ? ? ? ? ? Subscribe to Tel Aviv University's official YouTube channel to stay up to date on all our new videos, lectures and events: http://bit.ly/tauvod-sub Tel Aviv University's official website https://english.tau.ac.il/ Tel Aviv University on LinkedIn https://www.linkedin.com/school/tel-aviv-university/