SymRAG

Symmetry in Quantitative and Algorithmic Real Algebraic Geometry (SymRAG) was a research project at UiT The Arctic University of Norway, funded by the Tromsø Research Foundation (TFS) as part of the Pure Mathematics in Norway programme run together with the Trond Mohn Foundation. It was hosted by the Department of Mathematics and Statistics and led by Cordian Riener. The project ran in two phases from March 2018 to December 2024.

Symmetry, in its most basic mathematical sense, is invariance under the action of a group: rotations, reflections or permutations that leave an object unchanged. SymRAG set out to understand what this simple idea can do for polynomial systems – how the symmetries of a problem can be used to describe the geometry and topology of real algebraic and semi-algebraic sets, to design faster algorithms, and to solve optimization problems – and, conversely, where symmetry is exactly what makes a computation hard. See Research for the main results.

The project in numbers

• 39 research papers by the principal investigator, postdocs and PhD students
• 3 postdoctoral fellows and 1 PhD student funded directly; a further 5 PhD students, 2 postdocs, 8 master's students and 2 bachelor's students engaged through related activities
• approximately 14 MNOK in additional third-party funding raised on the basis of the project
• 4 international conferences, 3 summer schools and a series of smaller meetings organized in Tromsø and elsewhere
• the Lie–Størmer Centre for fundamental structures in computational and pure mathematics, which grew out of the project

The project ended in 2024. This site is kept as a permanent record of what it did and who was involved. The final report to the Tromsø Research Foundation (PDF, February 2025) gives a full account.