This workshop aims to unite leading experts and emerging researchers in the fields of minimal dynamics, renormalization, and C∗-algebras to explore cutting-edge advancements and foster interdisciplinary collaboration. By bringing together these communities—who rarely have the opportunity to engage directly—the workshop will provide a unique forum for the exchange of ideas and the cross-pollination of methods. Participants will showcase recent developments and establish connections between seemingly distinct areas, promoting a deeper understanding of shared mathematical structures. The central focus of the workshop will be the study of topological invariants, such as cohomology and K-theory, and their roles in diverse contexts including dynamical systems, operator algebras, and mathematical physics. These invariants serve as powerful tools for capturing and classifying intricate properties of systems, and their study has profound implications across mathematics and physics. By highlighting these connections, the workshop will pave the way for new insights and collaborations, driving progress at the interface of these vibrant research areas.