Probability, Ergodic Theory, Mathematical Physics Seminar

Meyer sets and topological eigenvalues

Daniel Coronel, Pontificia Universidad Católica de Chile

Friday, March 30th, 2018
3:00 PM - 4:00 PM
Hylan 1106A

Meyer sets were introduced by Yves Meyer in the 70’s in connection with questions in harmonic analysis and, after the discovery of quasicrystals by Schechtman in 1984, Meyer sets have also been used as a model for them. A key feature of quasicrystals is that they show sharp Bragg peaks in their X-ray diffraction, and it is known that this is related to the existence of eigenvalues for the dynamical system associated with the hull of the quasicrystal.

In 2012, Sadun and Kellendonk proved that a repetitive Meyer set in R^d has d linearly independent continuous eigenvalues. Their proof is based on the study of the pattern equivariant cohomology of the Meyer set. In this talk we give a dynamical proof of this result using a version of Gottschalk-Hedlund Theorem on the transverse space (groupoid) of the hull of the Meyer set.

Event contact: sevak dot mkrtchyan at rochester dot edu