Explore the optimization of Takens-type embeddings for time series analysis using persistent (co)homology in this 56-minute lecture. Delve into the process of carrying information about the topology and geometry of time series dynamics through embeddings. Learn how continuous optimization over persistence diagrams can be utilized to find optimal embeddings for periodic, quasi-periodic, or recurrent behaviors. Discover a practical approach to identifying effective embeddings, and gain insights into the current understanding of embedding spaces. Examine open questions in the field and explore the collaborative research conducted with Primož Škraba on this topic.