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This lecture explores persistent homology of function spaces and geometric metaphors in biology. Learn what persistent homology of function spaces means and discover recent results inspired by elementary biochemistry, including the solution to a problem posed by Misha Gromov in the 1970s. Examine two common geometric metaphors in biology—landscapes and networks—and consider the questions that arise from this perspective. The mathematical content is based on joint work with Jonathan Block and Fedya Manin, while other aspects involve collaboration with Rich Carthew, Lorenzo Orechia, Sam Riesenfeld, Ryan Robinett, and Evan Gibbs.
