Martina Scolamiero: Multidimensional Persistence and Noise.

Multidimensional persistence is a method in topological data analysis which allows to compare various measurements on a data set. Within this method a dataset is represented by a functor from the poset of r-tuples of non negative rational numbers to the category of vector spaces. Such functors are well behaved and we call them tame and compact. In this talk I will explain a way of comparing tame and compact functors based on the notion of a noise. This approach is based on the idea that in multidimensional persistence it is possible not only to choose properties of a dataset we want to study, for example by using filter functions, but also what should be neglected. I will also introduce an invariant for tame and compact functors we call the basic barcode. Finally, stability properties of the basic barcode and computational aspects will be addressed. (Joint work with W.Chacholski, A.Lundman, S.Oberg, R.Ramanujam)