Codes, arithmetic and manifolds

Prof. M. Kreck (Universitaet Bonn)

Friday 5th October, 2012 15:00-16:00 325


I will explain the concept of error correcting codes. This is so simple that one wonders why not everything is known. To indicate that this is completely wrong I will explain a relation between so called self dual codes and unimodular lattices, which lead to very difficult problems in analysis. On the way very important lattices like E_8 or the Leech lattice will occur. Thus codes are very complicated. In such a situation it might be of interest if codes occur in a completely different mathematical context. I will describe how codes occur in topology and present results about the question, which codes come from topology. This leads to a new construction of self dual codes. If time permits I will consider codes over the ring of Gaussian integers mod 2, which come from manifolds and are related to abelian varieties.

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