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Quasicrystals and almost periodic functions

Mariusz Zając (1999)

Annales Polonici Mathematici

We consider analogies between the "cut-and-project" method of constructing quasicrystals and the theory of almost periodic functions. In particular an analytic method of constructing almost periodic functions by means of convolution is presented. A geometric approach to critical points of such functions is also shown and illustrated with examples.

Quaternionic geometry of matroids

Tamás Hausel (2005)

Open Mathematics

Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper...

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