October 17, 2025
Title: New h-Principles in [split]G2, Symplectic, Contact and Other Geometries
Speaker: Laurence Mayther (Cambridge)
An exterior form is termed stable if its algebraic properties are preserved by all sufficiently small perturbations. Stable forms are fundamental to the study of G2/[split]G2 geometry and symplectic geometry, and additionally play a key role in the study of other geometries of interest, such as contact geometry.
In this talk, I shall introduce a new, general method for proving h-principles for stable forms, building on Gromov's technique of convex integration, and use this new method to prove 4 new h-principles related to [split]G2, symplectic and contact geometries. Applications to the non-constructability of compact [split]G2 and symplectic manifolds via geometric flows will then be discussed. Time permitting, I shall also explain (i) how this new method for proving h-principles subsumes all similar, previously established h-principles, and (ii) how this method may be extended to prove a fifth new h-principle in 6-dimensions related to para-complex geometry.