Algebra ist einer der klassischen Teilbereiche der Mathematik. Wir vertreten diesen Bereich in Forschung und Lehre und stellen damit die theoretischen Grundlagen zur Verfügung, die Anwendungen in vielen anderen Bereichen der Wissenschaft finden.
Unser Institut deckt mehrere Themen aus der Algebra ab. Ein Schwerpunkt unserer Arbeit ist die Computeralgebra, das heisst die Entwicklung von Algorithmen zur automatischen Lösung algebraischer Probleme. Ein weiterer Arbeitsschwerpunkt ist die Universelle Algebra, wo man sich mit abstrakten Verallgemeinerungen der klassischen algebraischen Strukturen beschäftigt. Ein dritter Schwerpunkt ist schließlich die Theorie der Fastringe, die in den vergangenen Jahrzehnten maßgeblich in Linz entwickelt wurde.
Institut für Algebra
Johannes Kepler Universität Linz
Altenberger Straße 69
Science Park 2, 3. Stock, Raum 372
DI: 12.00 - 17.00 Uhr
MI: 07.30 - 15.30 Uhr
DO: 13.00 - 18.00 Uhr
Manuel Kauers has been appointed member of the editorial board of Mathematics of Computation, a journal published by the American Mathematical Society.
The journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods.
Besides this journal, Prof. Kauers is also serving on the editorial board of the Journal of Symbolic Computation, Advances in Applied Mathematics, Journal of Computational Algebra, Annals of Combinatorics, and the Journal of Systems Science and Complexity.
Springer has just released a new textbook by Manuel Kauers about D-finite Functions.
We are pleased to announce that Clemens Hofstadler has successfully defended his Ph.D. studies today. His thesis was written under the joint supervision of Prof. Georg Regensburger and Dr. Clemens Raab. It was started when Georg was still a member of the Institute for Algebra. When he moved to Kassel, Clemens moved with him. The work was sponsored by Regensburger's FWF grant "Symbolic Computation for Identities of Operators". In his thesis, Clemens extends and generalizes modern algorithms for computing Gröbner bases to a non-commutative setting. He applies such general Gröbner bases in order to obtain concrete proofs of abstract operator identities.
Clemens will soon return from Kassel to Linz and join the Institute for Symbolic Artificial Intelligence led by Prof. Seidl. We congratulate Clemens on his achievements and wish him all the best for his future.
We are pleased to announce that our colleague Jakob Moosbauer has successfully defended his Ph.D. studies today. His thesis was written under the supervision of Manuel Kauers, and he was financially supported by the LIT AI Lab. As a member of this lab, Jakob developed new methods to search for better algorithms for multiplying matrices. Using the concept of flip graphs introduced in his thesis, he was able to set a new record for 5x5 matrices as well as some rectangular matrix formats. The thesis has resulted in several publications at high-rank venues in the area of computer algebra, including one ISSAC paper in 2023 which received the ACM Sigsam distinguished paper award. Jakob will soon move to the university of Warwick, where he will continue to work on matrix multiplication as a PostDoc in the group of Christian Ikenmeyer. We congratulate Jakob on his achievements and wish him all the best for his future.