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"Codes, arithmetic and manifolds" by Matthias Kreck
I will explain the problem behind codes. When sending and receiving information, errors can happen. One wants to reconstruct the original information from the received. This leads to 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 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. If time permits I will explain how codes occur in a very natural way in topology from manifolds with a bit symmetry. This leeds to a new construction of codes, which I will explain.