Main speaker 1999-2000:

Michael Baake is the main speaker of the Mark Kac seminar this year, and he will give three lectures in February, March and April. Here is the abstract for the series of three lectures:

The discovery of quasicrystals in the early eighties has triggered an intensive investigation of the various kinds of ordered states that are possible between periodic and random. In this series of lectures, I plan to describe the impact that quasicrystals had, focusing specifically on aspects of diffraction theory.

In the first lecture, I will start with the history of the field and summarize how and why quasicrystals challenged our understanding of the solid state. Some generalizations of crystallographic tools will be described that are suitable to cope with symmetry and equivalence concepts in this more general situation.

In the second lecture, I plan to survey mathematical diffraction theory, with special emphasis on the perfectly ordered systems. Of particular interest are point sets (representing atomic positions) which lead to pure point diffraction spectra, whose classification is far from complete.

In the third lecture, I will approach the diffraction of stochastic structures (such as random tilings) with methods from statistical physics. These systems show a variety of different spectral properties, including the possibility of practically relevant examples with singular continuous spectra.

For people that are interested, or have missed the first lecture by Michael Baake, we have a link to a postscript and pdf version of an introduction into the mathematics of quasicrystals.