• Study location R1-121
  • 2024-05-22 13:15–14:15

Julian Külshammer: Classifying submodules: from the Birkhoff problem to topological data analysis

Time: 2024-05-22, 13:15-14:15

Location: R1-121

Video link: https://mdu-se.zoom.us/j/69843890303 External link.

Participating: Julian Külshammer (Uppsala University)

Abstract: One of the fundamental theorems in algebra is the classification of finitely generated modules over principal ideal domains. It has as special cases Jordan normal form or the structure theorem for finite abelian groups. Given such a module, one can try to classify its submodules. This turns out to be a surprisingly hard problem, a special case of which is the Birkhoff problem posed in 1935. While our interest comes from algebra, the monomorphism category pops up in many places, e.g. in the theory of Cohen-Macaulay modules in algebraic geometry, or in topological data analysis, studying point clouds using topological invariants. In this talk, I will report on joint work with N. Gao, S. Kvamme and C. Psaroudakis on categorical tools towards solving this problem.

More information

For more information about the research milieu, please contact: