The Morse Landscape of the Lipschitz Functional

Explore a mathematical lecture that examines the Lipschitz constant as a height function on the space of maps between manifolds, investigating a question posed by Gromov nearly 30 years ago about its "Morse landscape." Discover whether homotopic maps require passing through higher Lipschitz constants when creating paths between them, and learn about higher-dimensional cycles in this space. The 46-minute talk from the Hausdorff Center for Mathematics presents joint work with Jonathan Block and Shmuel Weinberger, using persistent homology to formalize these concepts and share initial findings about the topological structure of the Lipschitz functional.