Computational challenges we face with multi-parameter persistence

I will start with presenting what I believe persistence is. Traditionally, persistence is associated with barcoding. This narrow view however is a serious obstruction to extending the notion of persistence to a multi-parameter setting. My aim is to propose a new way of looking at persistence and illustrate how it can be used to define stable invariants of multi-parameter data systems. I will then explain computational differences between 1- and multi-parameter situations