Primoz Skraba (6/10/20): Algebraically manipulating persistence modules (and a Minkowski-type bound) скачать в хорошем качестве

Primoz Skraba (6/10/20): Algebraically manipulating persistence modules (and a Minkowski-type bound)

Title: Algebraically manipulating persistence modules (and a Minkowski-type bound) Abstract: This talk will be mostly expository. I will go over different ways of thinking and manipulating persistence modules - examples include images, kernels, cokernels, etc. and the persistence that arises from these (and how we can think of them in terms of barcodes/diagrams). I will focus on persistence modules coming from homology and cohomology (rather than zig-zag persistence). Most of the talk will be a review of material which appears spread across the literature. Time permitting, I will discuss how persistence modules behave in exact sequences and provide upper and lower bounds on barcode decompositions.