Topological aspects in the theory of aperiodic solids and tiling spaces

Research Horizons Seminar
Wednesday, November 11, 2009 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 171
Jean Bellissard – School of Mathematics, Georgia Tech –
Craig Sloane
An assembly of atoms in a solid phase will be described through the notion of Delone sets and related to tilings. The Hull and the tiling space wiill be defined. It will be shown that the tiling space and the Hull can be constructed through an inverse limit of CW-complexes built out of the tiles and of the local patches. From then various cohomologies can be defined and allow to distinguish between these atomic distributions. The question of whether these topological invariant can be seen in experiments will be addressed.