Bi-Lipschitz Embeddings of the Space of Persistence Barcodes

The course covers the learning outcomes and goals of understanding optimal partial transport and transportation metrics for comparing measures with different total masses. It teaches the skills of working with the space of measures equipped with a specific metric and presenting results on the bi-Lipschitz embeddability of spaces into Hilbert space. The teaching method involves a talk introducing the concepts and presenting main results. The intended audience for this course is individuals interested in algebraic topology and transportation metrics.