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Drichlet analogues of q-series and some tiling patterns from quasicrystals

Host Institution:

La Trobe University

Title of Seminar:

Drichlet analogues of q-series and some tiling patterns from quasicrystals

Speaker's Name:

Dr Geoffrey Campbell

Speaker's Institution:

La Trobe University

Time and Date:

Friday 2nd September 2011, 2:00pm AEST

Seminar Abstract:

In writing new analogues for classical q series connected with Dirichlet series generating functions, the issue of natural interpretation of coefficients arose. Happily, many such interpretations have recently arisen in enumerative tilings that occur in the theory of quasicrystals. To be able to explain the concepts in a simple fashion, we shall mainly use two examples, discussed previously by Baake and Grimm, namely the triangular lattice, written as image007image008, the set (ring) of Eisenstein integers, and the vertex set of the twelvefold symmetric shield tiling, see Fig. 1. We concentrate on explicit results for these examples, and refer to original sources for a more general exposition and for details.

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Seminar Convenor:

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