Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory (15w5083)


David Damanik (Rice University)

(University of California Irvine)


The Casa Matemática Oaxaca (CMO) will host the "Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory (HALF)" workshop from September 27th to October 2nd, 2015.

The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for ``the discovery of quasicrystals'' --- materials with unusual structure, interesting from the point of view of chemistry, physics, and mathematics. In order to study electronic properties of quasicrystals, one considers Hamiltonians where the aperiodic order features are reflected either through the configuration of position space or the arrangement of the potential values. The spectral and quantum dynamical analysis of these Hamiltonians is mathematically very challenging. On the other hand, investigations of this nature are fascinating as one is invariably led to employ methods from a wide variety of mathematical subdisciplines. At present one understands very well the key quasicrystal models in one space dimension and the community is finally on the verge of making serious progress in the much more challenging higher-dimensional case by drawing on a new connection to yet another mathematical subdiscipline.

At this meeting, mathematicians from various areas and also some physicists will come together to push the boundaries of our understanding of mathematical quasicrystal models. The goals include a better understanding of the allowed energy levels of a quantum particle moving in a higher-dimensional quasicrystalline environment as well as the speed with which it does so.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.