Signed barcodes for multiparameter persistence

Moving from persistent homology in one parameter to multiparameter persistence comes at a significant increase in complexity. In particular, the notion of a barcode does not generalize straightforwardly. However, in this talk, I will show how it is possible to assign a unique barcode to a multiparameter persistence module if one is willing to take Z-linear combinations of intervals. The theoretical discussion will be complemented by numerical experiments. This is joint work with Steffen Oppermann and Steve Oudot.