## Seminario

Data evento:

Wednesday, April 27, 2016 - 16:00

Aula 1B1, pal. RM002

Seminario di Geometria

Anna Chiara Lai (Sapienza Università di Roma)

Tilings, quasicrystals and trigonometric inequalities.

Abstract:

Qruasicrystals are relatively dense, discrete sets characterized by the

ripetitivity of their patterns and, at the same time, by the lack of a

translational symmetry. Such structures emerge in medieval Arab art, in

the form of aperiodic mosaics, as well as in the molecular arrangement of

some alloys. A quasicristalline state of the matter was first observed by

Daniel Shechtman and for this discovery he was awarded of the Nobel prize

in Chemistry in 2011.

In this talk we overview the main properties of quasicrystals and the

techniques for their construction. We shall then focus on a result by

Mathei and Meyer, that establishes some trigonometric inequalities

(commonly referred to as Ingham type inequalities in the framework of

non-harmonic analysis) for a class of quasicrystals. We finally present a

new result, which extends such Ingham type inequalities to sets that can

be decomposed in the finite union of translations of a fixed lattice. In

the two dimensional case, this class of discrete sets includes well-known

tilings of the plane, such as the honeycomb lattice and all the regular

lattices. This talk is based on a joint work with Vilmos Komornik and

Paola Loreti.