Institute for Experimental Mathematics

Institute for Experimental Mathematics. It is a renowned research institution affiliated with the University of Duisburg-Essen, dedicated to advancing mathematical knowledge through computational and experimental methodologies. Founded in the early 1990s, it has become a central hub for interdisciplinary research bridging pure theory with practical computation. The institute's work spans several core areas of modern mathematics, contributing significantly to both academic fields and industrial applications.

History

The institute was established in 1992 under the leadership of its founding director, Gert-Martin Greuel, with strong support from the state of North Rhine-Westphalia and the German Research Foundation. Its creation was part of a strategic initiative to foster innovative, computation-driven mathematical research within the German academic landscape, notably following the merger that formed the University of Duisburg-Essen. Early collaborations with institutions like the Max Planck Institute for Mathematics and the Mathematical Research Institute of Oberwolfach helped solidify its reputation. Key figures in its development have included Gebhard Böckle and Michael Jünger, who have guided its evolution into a center for experimental algebra, geometry, and optimization.

Research focus

Primary research is concentrated on the interplay between algebraic structures, number theory, and high-performance computing. A major focus is on the explicit computation and exploration of objects in arithmetic geometry, including Galois representations and L-functions, often utilizing software like PARI/GP and Magma. The institute also maintains a strong program in discrete optimization and combinatorics, applying techniques to problems in graph theory and network design. This work frequently intersects with projects in coding theory and cryptography, investigating the mathematical foundations of secure communication. Computational experiments are conducted using the institute's own high-performance computing cluster, facilitating large-scale simulations in algebraic topology and geometric group theory.

Notable contributions

Researchers have produced groundbreaking software, most notably the Singular computer algebra system for polynomial computation, which is fundamental for work in algebraic geometry and singularity theory. The institute's team has made seminal advances in classifying modular forms and computing associated L-functions, contributing to the broader Langlands program. In optimization, work led by Michael Jünger has provided state-of-the-art solutions to the traveling salesman problem and linear ordering problem, with implementations used by companies like Bosch and Siemens. Collaborative projects have also yielded new algorithms in integer programming and insights into the structure of error-correcting codes, influencing standards developed by the Institute of Electrical and Electronics Engineers.

Organizational structure

The institute operates as an independent central institution of the University of Duisburg-Essen, with its director reporting directly to the university's rectorate. Research is conducted within several focused working groups, typically led by senior scientists or professors, covering areas such as Algorithmic Algebra and Discrete Optimization. It hosts a continuous stream of postdoctoral researchers and PhD students, many funded through programs of the Deutsche Forschungsgemeinschaft. The scientific staff often hold joint appointments with the university's Faculty of Mathematics, teaching advanced courses and supervising theses. An international scientific advisory board, featuring mathematicians like Peter Bürgisser and Eva Viehmann, provides strategic guidance on research directions.

Collaborations and partnerships

The institute maintains a dense network of academic partnerships, including long-term joint projects with the University of Oxford, the University of California, Berkeley, and the Tokyo Institute of Technology. It is a key node in several European Research Council grants and DFG priority programs, such as the Schwerpunktprogramm "Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory." Industrial collaborations have been established with technology firms like Deutsche Telekom on network optimization and with SAP SE on data analytics. The institute also co-organizes major conferences, such as the annual International Congress on Mathematical Software, and regularly hosts visiting scientists from institutions like the Institute for Advanced Study and the École Polytechnique.

Category:Research institutes in Germany Category:Mathematical organizations Category:University of Duisburg-Essen