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Explore open problems related to Vietoris-Rips complexes in this comprehensive lecture by Henry Adams. Delve into the fascinating world of applied algebraic topology, where mathematicians are categorized as "birds" who connect broad theories, and "frogs" who solve specific problems. Discover attractive challenges for both types of mathematicians, including the homotopy types of Vietoris-Rips complexes for various geometric objects and spaces. Uncover emerging connections between Vietoris-Rips complexes and diverse areas of pure mathematics, such as metric geometry, quantitative topology, measure theory, topological combinatorics, geometric group theory, and geometric topology. Gain insights into the mathematical properties of Vietoris-Rips complexes and their applications in approximating dataset shapes. Access accompanying slides for a visual understanding of the concepts presented in this engaging 1-hour 18-minute talk from the Applied Algebraic Topology Network.
