July 10, 11:30 ~ 12:30
Interpolation, rudimentary geometry of spaces of Lipschitz functions and complexity.
University of Chicago, USA - firstname.lastname@example.org
This talk will interweave (and hopefully motivate) three themes. The first theme is interpolation. Lipschitz functions are built to be well approximated by interpolations from samples. Analogous, but more difficult, is topological interpolation: inferring a manifold (or its properties) from samples. The second theme is geometric: what do spaces of Lipschitz functions look like, especially when they are nonlinear, i.e. the target is not a vector space? What can we say about Gromov-Hausdorff spaces of manifolds? The final theme is quantitative geometric topology, i.e. the complexity of objects or homeomorphisms that topologists infer.
Joint work with Greg Chambers (Rice, USA), Sasha Dranishnikov (Florida, USA), Dominic Dotterer (Stanford, USA), Steve Ferry (Rutgers USA) and Fedor Manin (Ohio State, USA).