17 Dec 2024. 14:00 CET. Talk by Álvaro del Pino.
Abstract: The h-principle is the subfield of Differential Topology dedicated to the classification problem for geometric structures on manifolds, up to homotopy. Statements in h-principle are often of the form: “The space of structures of type X is weakly homotopy equivalent to some other space of algebraic-topological nature”; the latter space is therefore susceptible to being studied with homotopy theoretical tools. This approach has been extremely successful in the study of mappings with prescribed singularities (for instance immersions and submersions), foliations, symplectic and contact structures, and metrics with various curvature constraints.
The aim of the talk is to explain what the h-principle is and what it can do, in broad strokes. As we go along, I will try to indicate possible open questions (with h-principle flavor) adjacent to the field of generalized geometry.