Title: Diagrams of Persistence Modules Over Finite Posets
Speaker: Aziz Burak Gulen (OSU)
Speaker's URL: https://math.osu.edu/people/guelen.1
Abstract: Starting with a persistence module – a functor M : P → Veck for some finite
poset P – we seek to assign to M an invariant capturing meaningful information
about the persistence module. This is often accomplished via applying a M¨obius
inversion to the rank function or birth-death function. In this talk, I will establish
the relationship between the rank function and birth-death function by
introducing a new invariant: the kernel function. The persistence diagram produced
by the kernel function is equal to the diagram produced by the birth-death
function off the diagonal and we prove a formula for converting between the persistence
diagrams of the rank function and the kernel function. Moreover, the
diagram assignment to the kernel functions is functorial when the morphisms
between persistence modules are defined via Galois connections. This is joint
work with Alex McCleary.
URL associated with Seminar
https://tgda.osu.edu/activities/tdga-seminar/
Zoom: https://osu.zoom.us/j/93628189417?pwd=a0l3aU5OM3Z6U09lZFllYlJ0Tis0QT09
