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Faculty of Mathematics and Computer Science |
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Research Activities at the Faculty |
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Reports of the Institutes |
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Research Activities at the Faculty |
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The Faculty of Mathematics and Computer Science is divided into the Mathematical Institute and the Institute of Computer Science. The Mathematical Institute has a proud history of mathematical research stretching back over a century. The Institute of Computer Science emerged from the Department of Computer Science founded at the University of Leipzig in 1989, and has been completely restructured in line with the process of reorganisation undergone by the University over the past decade. Both institutes are subdivided into departments in which one or more professors and other members of faculty collaborate. |
Mathematical Institute |
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Mathematical Institute At the Mathematical Institute, the Chair of Numerical Mathematics and Scientific Computing (C4) became vacant in 1999 when the former holder accepted an appointment at Zurich University. Both this position and the chair of Discrete Mathematics (C4) have been advertised. Moreover, the Faculty has decided upon a proposal for the appointment of the chair of Theoretical Mathematics. Research at the Mathematical Institute is carried out in the Departments of Algebra, Analysis, Didactics, Geometry, Functional Analysis/Mathematical Physics, Numerical Mathematics/Scientific Computing, Optimisation, and Mathematical Economy/Stochastics. It deals with areas such as:
Various research activities have been financially supported by the DFG (German Science Foundation), the DAAD (German Academic Exchange Agency), and the EU. In both research and education, strong co-operation ties between the Mathematical Institute and the Max Planck Institute of Mathematics in the Sciences have been nurtured over the past years. Joint research seminars and workshops (for example on geometry, analysis, neural networks/cognitive systems, mathematical physics, microstructures) have been organised, and series of lectures on current research topics have been given at the Mathematical Institute by Profs Jürgen Jost, Stefan Müller and Eberhard Zeidler of the Max Planck Institute. In November 1999, the conference "Prospects in Geometry" was held at the Max Planck Institute of Mathematics in the Natural Sciences, where internationally recognised experts reported on current developments in differential geometry and related areas. This conference, the fourth in a series of conferences since 1996, was jointly organised by the Max Planck Institute (Prof. Mathias Schwarz) and the Mathematical Institute (Prof. Hans Bert Rademacher). To mark the centenary of the death of Sophus Lie (ordinarius at the Mathematical Institute of Leipzig University 1886-1898), a conference entitled "100 Years after Sophus Lie" was held at the University of Leipzig. It was organised by Profs Klaus Beyer and Konrad Schmüdgen (Mathematical Institute) and Jürgen Jost (Max Planck Institute of Mathematics in the Natural Sciences). One of the aims of the conference was to heighten awareness of the life and work of this eminent mathematician among present-day mathematicians and students. Despite its enormous importance and the large number of applications in the sciences, Lie's work is still not completely accessible owing to its depth and complexity. The conference was designed to present modern research on Lie theory. Generating great interest in Germany and abroad, the conference was attended by a broad spectrum of participants presenting papers on mathematics, the history of science, and theoretical physics, and boosted the University's past and current reputation as an important place of science. The more than 100 participants included some very eminent scientists who have made major contributions to the development of Lie theory in the 20th century, such as Prof. Armand Borel (Princeton University), Prof. Sigurdur Helgasson and Prof. Bertram Kostant (MIT Cambridge). In their addresses, they described the development of Lie's theories and ideas up to their own recent findings. Further topics were related to Lie groups and complex analytic supermanifolds, new classes of infinite-dimensional Lie algebras, renormalisation groups in theoretical physics, and commutative homogeneous spaces of Lie groups. In November 1999, a colloquium was held to celebrate the 150th anniversary of the birth of Felix Klein, the founder of the Mathematical Seminar in Leipzig. Addresses were given by Dr Rüdiger Thiele (Karl Sudhoff Institute of the University of Leipzig) on Felix Klein in Leipzig and by Prof. Peter Slodowy (Hamburg University) on Platonic bodies, Klein singularities and Lie groups. The DFG has approved a proposal to set up a graduate programme (postgraduate research unit) entitled "Analysis and Geometry, and their Interaction with Science" in May 2000. The programme is designed to ascertain the mutual relations between mathematics and the sciences, and to use them in training doctoral students. This is an area where nowadays much needs to be done owing to the extensive separation of mathematicians from other scientists in graduate courses. The research programme is roughly divided into an analytical and a geometrical section - subjects which have a strong history at the Mathematical Institute. Leipzig's particular strength lies in the relations with the sciences maintained by more than just those disciplines generally considered to belong to applied mathematics. Research focuses on aspects of material science, hydrodynamics, thermodynamics and statistical mechanics, classical mechanics, image-processing, neural networks, and the general theory of relativity. The research programme is characterised by variational methods, the interplay between geometry, global analysis, and partial differential equations, and the close links between analysis, numerical mathematics and mechanics. |
Institute of Computer Science |
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Institute of Computer Science The Institute of Computer Science currently has nine regular academic chairs covering the following areas of instruction and research:
A tenth chair (Applications-specific information systems) is in the process of being filled. Two honorary academic chairs have also been established in:
The number of students reading computer science continued to grow, from 516 at the start of the 1998/1999 winter semester to 657 a year later (including 516 on the computer science diploma programme). Despite the extra burden, notable research findings were achieved, and interdisciplinary co-operation both within and outside the University of Leipzig was expanded. At the Institute of Computer Science, numerous research projects were successfully continued and new projects were begun. In 1999 the number of publications rose compared to the previous year, comprising: 4 books Funding also increased. That received from the DFG, the BMBF (German Ministry of Education, Science, and Research) and industry totalled DM1,228,000 (compared to DM933,000 in the previous year). In addition, grants were received from the HBFG (Higher Education Construction Assistance Act), while research funding was supplied by the SMWK (Ministry of Higher Education, Research and Culture of the Free State of Saxony) and HSP3 (Higher Education Special Programme III). Overall, the research funding used at the Institute increased from DM1.9 million to 2.2 million - more than DM70,000 for each scientific position funded by the state. At present, more than 30 scientists are being financed by grants and scholarships, in addition to the current 12 scholarship-holders on the postgraduate research unit "Knowledge Representation". Some of the co-operative research activities are briefly described below. A more detailed presentation of individual projects can be found in the annual reports of the Institute and the University (also available on the internet at www.informatik.uni-leipzig.de). Within the University of Leipzig, the Institute is involved in projects with other departments and facilities such as:
Seven of the 12 university instructors involved are from the Institute of Computer Science, including the spokesman, Prof. Brewka. Institutes from three other departments are also participating, namely the Institute of Medical Informatics, Statistics and Epidemiology (IMISE), the Institute of Business Computing, and the Institute of Logic and Philosophy of Science. The contents of the investigations range from theoretical foundations to complex areas of application for knowledge representation. The subject of research for the postgraduate research unit is the representation and processing of knowledge. Although new theoretical findings from the area of philosophical logic and the theory of science as well as fundamental research in artificial intelligence have not been utilised to a great extent in concrete application systems, the technical requirements in the areas of representation and processing from concrete application issues are often insufficiently considered by theorists. One of the main goals of the graduate programme is thus to build a bridge in the graduate student's training from the fundamental issues of knowledge representation to the technical implementation of corresponding methods and concrete application in the areas of information management and medical computer science. The concept of knowledge representation is deliberately viewed in broad terms: in addition to the representational formalisms and languages as well as their applications and techniques, it also includes the integration of various sources of knowledge and their visualisation. All of these aspects are necessary prerequisites for the successful use and acceptance of knowledge-based techniques.
In the year under review, the Institute of Computer Science (Prof. Rahm and Prof. Saupe) developed a concept for instruction and research in the area of biocomputer science at the University of Leipzig together with colleagues from the biological sciences (Prof. Schlegel and Prof. Hahn), medicine (Prof. Löffler), and the Max Planck Institute of Evolutionary Anthropology (Prof. Pääbo, Prof. von Haeseler). The concept has received a positive evaluation from the DFG as part of a national call for proposals. A number of research projects are being worked on in co-operation with other universities, including participation in the following DFG priority programmes:
Prof. Irmscher is involved in a postgraduate research unit at his former university in Freiberg as well as the SMWK's centre of excellence "Telecommunication Service Applications for Industry and Administration" (with Chemnitz Technical University and Dresden Technical University). Internationally, there are numerous close contacts with scientists in Western and Eastern Europe, the USA, Canada, Japan, Africa and Australia. In addition, several industrial projects are being worked on, especially with companies participating in the LIV (Leipzig Computer Science Association). This Association is a forum for close co-operation with various companies and institutions in the region of Leipzig, and it gives regular presentations at trade fairs (e.g. CeBit, book fairs, BIK) etc. A number of professors at the Institute are conducting research into various issues of electronic media/multimedia which will be of increasing importance for the University as a whole. They include the HSP III project "Electronic Libraries" (Prof. Rahm), in which an internet-based document-server has been developed which is available to all University departments for the storage of various documents. In co-operation with the University Library and the University Computer Centre, it will be used in the future to provide online access to virtually all dissertations and doctoral theses written at the University ("Online Dissertations Project"). Other research work is included in the following list of projects with external support:
The rapid development of computer science at the University of Leipzig in the past few years, as characterised by the increase in the number of students, grants, scientists and research projects, has exacerbated many bottlenecks. This primarily concerns inadequate state funding, and a shortage of both staff and rooms. New premises are urgently required to house computer pools for the students, as well as offices for those employed in grant projects. The computer administration is beset by chronic shortages. |
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Research Report 1999 | |||||
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