/ Havard Bjerkevik: Computing approximate decompositions of multiparameter modules

Havard Bjerkevik: Computing approximate decompositions of multiparameter modules

October 21, 2025
4:30 pm - 5:30 pm

Abstract: In 2023, I introduced an invariant of multiparameter modules called the pruning, and used it to show a stabilized Krull-Schmidt theorem, demonstrating that multiparameter decomposition enjoys stability properties despite its wild instability in a naive sense. The pruning of M is a particularly decomposable module close to M, which is a property suggesting that it can be a useful tool to split almost-decomposable modules into smaller pieces, hopefully bringing some of the advantages of the one-parameter barcode to the multiparameter setting. I will first explain some of the theoretical background, then talk about work in progress with Jan Jendrysiak and Fabian Lenzen on computing the pruning in practice.