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Tilings, logic, quasicrystals, discrete geometry, long-range order,
and diffraction all come together in a remarkable confluence of
ideas. In the first (general) talk, we will begin with some of the
unexpected history of the subject of Aperiodic Order and discuss
some of the mathematics that it has generated, as well as some of
its outstanding problems.
We will touch on many areas: geometry, topology, measure theory,
dynamical systems, and algebra. However, the great thing about the
subject is the number of nice pictures that are relevant to it, and
I will show lots of them!
One of the interesting problems in this subject is to understand
what it means for a point set to be pure point diffractive. In the
second talk I would like to talk more about diffraction and go into
some details about what is known in the case of substitution
systems and how we know it. This talk will require a little more
mathematical background, but I will stay away from a lot of
technical details.
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