## Mathematics

Some main topics of my studies of mathematics and computer science were algebra, homological algebra, differential equations, mathematical physics, programming (Pascal, Ada and Java), software engineering and artificial intelligence. A graphics related to algebraic topology - the singular chain complex and its homology:

My diploma thesis in the area of quantum statistical mechanics and functional analysis with Prof. K.-H. Fichtner / Universität Jena (in German):

Groups of unitary operators and complete orthonormal systems
- A teleportation model in spaces of qubits -

The medium of teleportation is an entangled state: A coherent laser beam (or one single particle - with photons, teleportation experiments were successfull) is splitted into two parts, e.g. by a partly translucent mirror. Then the two parts remain interconnected to each other; a state measurement of one half beam immediately determines the measurement of the second. The speed of light is not relevant to this effect! (But for information transfer by teleportation, you need a supplementary message transmitted by 300.000 km/h at most.)

With "Canon 1 a 2 cancrizans" of J. S. Bach's Musical Offering, I found an analogy to this remarkable entangled state: The main theme and its contrapunctus are mirrored in the middle of the canon and running backwards. So if Bach would have changed one note anywhere, by one thought he would have been forced to change his mirror image. See the notes and listen to the music - repeat it not infinitely, but as often as you want! (A difference: the splitting takes place at the beginning of the physical entangled state.)

After my diploma I kept contact with the university of Jena. I concentrated on algebra studies - (reflection) groups and their representations, rings, modules, (Hecke) algebras, separability. Thereafter I wanted to learn more about applications: machine learning, data mining, algorithms of pattern recognition and AI, numerics and statistics.

Finally I rediscovered formal concept analysis, where clear and beautiful mathematics are connected to rich applications: algebraic structures of complete lattices are to be discovered in questions from knowledge representation, data mining, software engineering or semantic web - as well as in bioinformatics / systems biology. There my current research project is the modelling of gene regulatory networks.

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