Title: Bottleneck stable invariants of multiparameter persistence modules via relative homological algebra
Speaker: Luis Scoccola (Northeastern University)
Speaker's URL: https://luisscoccola.github.io
Abstract: Unlike one-parameter persistence modules, for which we have the barcode, persistence modules with two or more parameters do not admit a complete discrete invariant, and thus incomplete invariants must be used to study the structure of such modules in practice. The Hilbert function and the multigraded Betti numbers are among the simplest such incomplete invariants, and, although these invariants are already being used in applications, it is a priori unclear whether they satisfy a stability result analogous to the stability of the one-parameter barcode. I will present joint works with Oudot and with Botnan, Oppermann, and Oudot in which we prove bottleneck stability results for multigraded Betti numbers and the Hilbert function, as well as for finer invariants coming from projective resolutions in certain exact structures on categories of multiparameter persistence modules.
