- Series
- School of Mathematics Colloquium
- Time
- Thursday, October 17, 2013 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skyles 006
- Speaker
- Antoine Julien – Norwegian University of Sciences and Technology Trondheim, Norway
- Organizer
- Karim Lounici
In this talk, my goal is to give an introduction to some of the mathematics
behind quasicrystals. Quasicrystals were discovered in 1982, when Dan
Schechtmann observed a material which produced a diffraction pattern made of
sharp peaks, but with a 10-fold rotational symmetry. This indicated that the
material was highly ordered, but the atoms were nevertheless arranged in a
non-periodic way.
These quasicrystals can be defined by certain aperiodic tilings, amongst which
the famous Penrose tiling. What makes aperiodic tilings so interesting--besides
their aesthetic appeal--is that they can be studied using tools from many areas
of mathematics: combinatorics, topology, dynamics, operator algebras...
While the study of tilings borrows from various areas of mathematics, it
doesn't go just one way: tiling techniques were used by Giordano, Matui, Putnam
and Skau to prove a purely dynamical statement: any Z^d free minimal action on
a Cantor set is orbit equivalent to an action of Z.