The following two topic areas are available at the moment:

D-algebraic functions. These are functions defined as solutions of certain nonlinear differential equations. The task is to develop computer algebra algorithms that take a differential equation as input and return as output some useful information about its solutions. Such algorithms are needed for dealing with functions that cannot be expressed in terms of explicit expressions.

Matrix multiplication. The cost of matrix multiplication is a big unsolved problem in algebraic complexity theory. The task is to explore and further develop automated techniques for constructing better matrix multiplication algorithms. While completely resolving the mystery of matrix multiplication is too big a task for a Ph.D. thesis, it is certainly realistic to make some valuable progress in this direction.

The positions are financed by research projects recently granted by the Austrian Science Fund. They will be carried out at the Johannes Kepler University in Linz, Austria, where we are proud to provide excellent working conditions for doing research in computer algebra.

Applicants should have completed their Master's degree in mathematics or computer science. A strong background in algebra is required. Ideally, the applicant should also have some experience with computer algebra.

Please send your motivation letter, your CV, and a summary of your Master's thesis by email to manuel.kauers@jku.at.