Algebra is one of the classical branches of mathematics. We represent this area in research and teaching, providing the theoretical foundations that are used in many other areas of science.
Our institute covers several topics from algebra. One focus of our work is computer algebra, that is the development of algorithms for the automatic solution of algebraic problems. Another focal point of work is Universal Algebra, which deals with abstract generalizations of classical algebraic structures. A third focus is finally the theory of nearrings, which has been developed significantly in Linz in recent decades.
The next Linz Algebra Research Day will be held on June 15th.
In its board meeting on 10th May 2021, the Austrian Science Fund FWF has approved Thibaut Verron's grant application "Weighted-homogeneous structure in polynomial equations".
The project concerns the development of algorithms for solving systems of structured polynomial equations. Questions in this context include the design and implementation of algorithms taking into account the structure, as well as the study of their complexity. The proposed work has immediate applications for solving such structured systems, for example in physics.
Furthermore, a better understanding of the weighted-homogeneous structures could lead to algorithmic and complexity improvements regarding polynomial elimination, which is a crucial step in many algorithms manipulating systems of polynomial equations.
We are pleased to announce that another member of our institute has succeeded in getting a permanent position and will thus be able to stay in academia.
Hao Du came to Linz in 2019 as a postdoc of Christoph Koutschan at RICAM and joined the Institute for Algebra in January 2021, where she is currently employed on an FWF-financed project directed by Georg Regensburger. She received her PhD from the Chinese Academy of Sciences, whose strong symbolic computation group is closely collaborating with the various symbolic computation groups in Linz. In Summer 2021, she will return to Beijing and start as assistant professor at the Beijing University of Posts and Telecommunications.
We wish her all the best for her future career.