GRK 1632: Experimental and Constructive Algebra

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The underlying idea of the Graduate School ¿Experimental and Constructive Algebra¿ is the experimental study of algebraic problems at an advanced theoretical level. Motivated by difficult and partly abstract questions stemming from both pure mathematics and applied sciences, an experimental approach including the use of computers yields insight leading to both relevant theoretical results and innovative algorithmic methods.The research group in algebra at RWTH Aachen University has been doing pioneering work in computer algebra since 1968, e.g. through the development of the computer algebra systems GAP, CHEVIE and CARAT, and the contributions to the modular ATLAS project. Group theory is the focus of our research; it is the mathematical abstraction of the ubiquitous concept of symmetry. The computer functions as a microscope the mathematician uses in studying abstract objects experimentally. The continuing further development of relevant methods allows increasingly deep insight into the world of mathematics. At the same time it enables people in other areas to use the algorithms and results without having to master with the often difficult theory that lies beneath. As the first period has shown this experimental approach provides a direct path for the young doctoral students to understanding abstract mathematical concepts.The second characteristic of this Graduate School is its cross cutting nature. The participating researchers work in different areas of mathematics which nonetheless are joined by numerous connections. These connections are expanded and strengthened in this Graduate School. The resulting synergistic effects yield innovative approaches and alternative points of view, leading to substantial improvements beyond the algorithmic methods. Both the constructive approach and the concept of symmetry are unifying common principles. Every dissertation lies at the intersection of at least two different research areas of the participating professors and is actively supervised by at least two professors. The insight into methodologically and thematically different fields ensures a broad education of the doctoral students and also enriches the scientific perspective of the supervisors.