- Salón K201 (antes salón de usos múltiples del nivel H), CIMAT, Guanajuato
13:00 - 14:00. Stratifying multi-parameter persistent homology
Nina Otter, Oxford University
Abstract: In their paper "The theory of multidimensional persistence", Carlsson and Zomorodian write "Our study of multigraded objects shows that no complete discrete invariant exists for multidimensional persistence. We still desire a discriminating invariant that captures persistent information, that is, homology classes with large persistence."
In this talk I will discuss how tools from commutative algebra give computable invariants of multi-parameter persistence modules, which are able to capture homology classes with large persistence. Specifically, multigraded associated primes provide a stratification of the region where a multigraded module does not vanish, while multigraded Hilbert series and local cohomology give a measure of the size of components of the module supported on different strata. These invariants generalize in a suitable sense the invariant for the one-parameter case. This talk is based on joint work with Hal Schenck, Heather Harrington and Ulrike Tillmann.