Dear colleagues and students,

I am able to offer a position for working on a PhD thesis in the area of Gröbner under my supervision. Details can be found at

http://www.dk-compmath.jku.at/

and in the attached announcement. Deadline of application is May 15, 2008. The position is available in the frame of a new Doctorate Program on "Computational Mathematics" offered by RISC in cooperation with Numerical Computation Groups at the Johannes Kepler University, Austria.

The goal of the thesis is a thorough presentation of the theory and algorithmics of noncommutative Gröbner bases in a completely formal (logic) frame, namely the Theorema version of predicate logic. In the first part of the thesis, using and extending the Theorema automated formal reasoning tools, the theory should be formally verified and, using the Theorema functor programming paradigm, the algorithmics should be implemented in a generic, and also formally verified, way. The subtle relation of (noncommutative) Gröbner bases theory with linear algebra based on the notion of generalized Sylvester matrix, which has significant potential for improving the algorithmics but is not yet sufficiently studied theoretically, should be investigated in detail using the formal theory and the formal exploration tools provided in the first part of the thesis. One major application of noncommutative Gröbner bases theory, e.g. cryptography, should be explored and implemented. The thesis will also serve as an important input into a major research project "Math Journals as Active Reasoning Agents" by the same proposer in cooperation with a renowned international mathematics publishing company and will be carried out in close cooperation with the currently most active research groups in noncommutative Gröbner bases theory worldwide.

I ask my colleagues to make this announcement known to students interested. Applications should be submitted through the above web site. If there are questions, write directly to my: bruno.buchberger@jku.at.


Bruno Buchberger, Dr.phil. Dr.h.c.mult.
Professor of Computer Mathematics
Head of Softwarepark Hagenberg

Research Institute for Symbolic Computation
Johannes Kepler University
A4232 Schloss Hagenberg
++ 43 664 4211646
bruno.buchberger@jku.at
www.risc.uni-linz.ac.at/people/buchberger