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
Adresse
Johannes Kepler Universität Linz
Altenberger Straße 69
4040 Linz
Standort
Science Park 2, 3. Stock, Raum 372
Öffnungszeiten Sekretariat
DI: 12.00 - 17.00 Uhr
MI: 07.30 - 15.30 Uhr
DO: 13.00 - 18.00 Uhr
Telefon
In its most recent board meeting, the Austrian Science Fund FWF has granted a research project on "Constructive Decomposition of Matrix Multiplication Tensors". The project was proposed by Manuel Kauers in collaboration with Jakob Moosbauer.
The goal of this project is the development of advanced search techniques for writing a given tensor as a sum of rank-one tensors. This is the key step in the development of fast matrix multiplication algorithms.
In its most recent board meeting, the Austrian Science Fund FWF has granted a research project on "The Elekes-Szabo Problem". The project was proposed by Oliver Roche-Newton and Audie Warren, who will also serve as principal investigators.
The Elekes-Szabó Theorem gives an upper bound for the size of the intersection between an algebraic surface and a Cartesian product, subject to certain non-degeneracy conditions on the surface. This rather general theorem has led to many beautiful applications, particularly in discrete geometry. The goals of this project include establishing a version of the Elekes-Szabó Theorem in the finite field setting, and exploring further applications of this result, particularly in the context of sum-product phenomena.
In its most recent board meeting, the Austrian Science Fund FWF has granted a research project on "Algorithms for D-Algebraic Functions". The project was proposed by Manuel Kauers, who will also serve as principal investigator.
The general goal of the project is the development of algorithms for functions and power series defined by nonlinear differential equations. While solutions of linear differential equations have been intensively studied in computer algebra, and many sophisticated algorithms are available for them, the nonlinear case has not received that much attention yet. In the project, this case will be put into the focus.
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.