Explore a novel topological-data-analytical (TDA) method for identifying small density vacuums surrounded by high-density regions in this 30-minute conference talk. Delve into the robust and provable approach, examining its theoretical foundations and practical applications through simulations. Learn about the rigorous bounds on the persistence of these vacuums and gain insights from the collaborative work of Chunyin Siu, Gennady Samorodnitsky, Christina Lee Yu, and Andrey Yao. Access the accompanying preprint and presentation slides for a comprehensive understanding of this innovative TDA technique.