Explore the intricacies of decomposing simplicial complexes in this 48-minute lecture by Francesca Tombari from the Applied Algebraic Topology Network. Delve into the challenges of maintaining homotopy type during decomposition and reassembly, and discover how obstruction complexes can provide insights into these changes. Learn about the relationship between a simplicial complex's homotopy type and its decompositions, with practical demonstrations using Vietoris-Rips complexes. Covering topics from introductory examples to the general case and applications, gain a comprehensive understanding of this collaborative research involving Wojciech Chachólski, Martina Scolamiero, and Alvin Jin.