The START group has emerged from Peter Paule's research group on algorithmic combinatorics. It was established in 2009 when the START prize of the Austrian federal minister of science and research was awarded to Manuel Kauers. The prize is equipped with funding for up to four group members for up to six years. The official start of START is scheduled for April 1, 2010. (No April's fool.)
In the new START group, we will be doing research in computer algebra related to special functions, differential and difference equations, symbolic summation and integration, Gröbner bases, and inequalities. On these and related topics, there are three general tasks that we want to address:
Constructing efficient algorithms. We want to find asymptotically fast algorithms for solving questions about special functions. Research of the past decades (at RISC and elsewhere) has led to a variety of algorithms that are able to perform spectacular simplifications of complicated symbolic sums and integrals. But if expressions exceed a certain size, the computational cost of these algorithms becomes prohibitive. Our goal is the construction of algorithms that are well suited for dealing with big input.
Developing fast software. We want to implement these algorithms in free and open software packages. Turning theoretical efficiency into practical efficiency is a difficult task, but it is well worth the effort, because it is often only the experience gained from observing the behaviour of actual programs which can lead to the discovery of new and substantial theoretical improvements. Our goal is therefore the development of software that is capable of handling big input.
Solving hard problems. We want to apply this software to actual open problems that are of independent interest. Software for special functions has already solved many challenges in the past, and it will be possible to solve many more of them with high performance software. Our goal is to knock out problems concerning special functions that arise in number theory, in combinatorics, in engineering, in physics, or elsewhere, but which are too hard for presently available tools because they lead to big input.
Open Positions for Ph.D. Students
We are looking for candiates who are interested in joining us in this effort and in doing their Ph.D. in the START group. Embedded into the ordinary RISC Ph.D. curriculum, START students will receive general education in symbolic computation and pursue an individual research project at the forefront of computer algebra, which is likely to have high impact in several different areas of mathematics, natural sciences, and engineering. We offer the rare combination of
the pioneering atmosphere of a freshly founded team of young researchers working on the hot topics of the research area, and
the traditional environment of a world-famous institute with scientific connections and partners in all parts of the world.
We encourace highly motivated candidates with interest in both mathematics and computer science, a Master's degree in one of these fields, and, preferably, some knowledge of computer algebra, to get into contact with Manuel Kauers no later than January 31, 2010.
Bachelor Theses, Master Theses, and Internships
In the frame of the START project, there will be a continous supply of possible topics for bachelor and master theses, or for (scientific) internships. Also some (limited) financial support is available for students contributing to the START project on undergraduate level.
Interested candidates are welcome to get into contact with Manuel Kauers.
For further information, write to Manuel Kauers.
Please quote 10 Academic Resources Daily in your application to this opportunity!