Complexity of invariant theory of quiver representations

• Applicants: Professor Dr. Peter Bürgisser; Professor Dr. Michael Walter
• Subject Area: Mathematics ; Theoretical Computer Science
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 556164098

Quiver representations connect to a wide range of mathematical problems and applications. Their theory rests on the trichotomy into finite representation type, tame, and wild type, the latter considered hopeless from a classification point of view. However, recently, it was discovered that algorithms can provide efficient answers to orbit (closure) problems even in wild cases. The goal of our project is to explore this phenomenon further. For example, is there an efficient algorithm for Horn's problem not only deciding feasibility, but also constructing witnessing matrices? A major motivation is to view quiver representations as a highly illustrative testing ground for algorithmic and complexity theoretic problems that recently have been posed in the much more general setting of "non-commutative optimization".

• DFG Programme: Research Grants