Online seminar, Tuesday at 10:00, U. Haifa Topology & Geometry seminar on April 21, 2020
Geometry & Topology Seminar
Speaker: René Rühr (Technion)
Topic: Counting in Cut-And-Project Quasicrystals
Place: This is an online seminar.
Date: Tuesday, April 21, 2020
Abstract:A cut-and-project set is constructed by projecting (part of) a lattice in Euclidean space to some subspace. These point sets constitute an important example of so-called quasicrystals. We shall describe counting result for patches in generic cut-and-project sets which will follow from generalizing certain L^2 discrepancy bounds for lattices due to Rogers and Schmidt from the 50’s. During the talk, we shall present some classification results of the moduli spaces of cut-and-project sets introduced recently by Marklof-Strömbergsson. These are obtained by considering the orbit closure of the special linear group in d-space acting on a lattice L inside the space of unimodular lattices of rank d+m. Theorems of Ratner imply that these are meaningful objects. Based on joined work with Yotam Smilansky and Barak Weiss.