virtuell

There is no rigorous mathematical definition of a quasicrystal. In spaces with some group translation the latter term usually refers to well-scattered point sets (Delone sets) that are not periodic but display long range symmetries. Classes of these sets such as model sets have already been studied by Meyer in the 70's, i.e. some time before Shechtman's discovery of physical alloys with non-periodic molecular structure in 1982 (Nobel prize for chemistry in 2011). In this talk we focus on non-periodic point sets in lcsc groups (with the Heisenberg group as a guiding example) that are not too far from crystals in a dynamical sense. The main focus will be on the generalization of the concept of linearly repetitive Delone sets known from Euclidean space. Although they are not found easily, non-periodic, linearly repetitive Delone sets exist in many non-Abelian groups as well. Going beyond a result from Lagarias and Pleasants for R^d roughly outline how to prove unique ergodicity for the associated dynamical systems for a class of Lie groups of polynomial volume growth. Joint work with Siegfried Beckus and Tobias Hartnick.

Hörer sollten sich bitte im Moodle-Raum https://moodle.tu-dortmund.de/enrol/index.php?id=23191 des Seminars anmelden. An alle Angemeldeten werden die Zugangsdaten zum meeting geschickt Weitere Vorträge in der Reihe sind unter http://www.mathematik.tu-dortmund.de/lsix/lehre/WiSe2021/GRK-Seminar/index.php einsehbar.

Felix Pogorzelski

Universität Leipzig