I will explain how to introduce a Frobenius twist in the construction of Fukaya category by equipping the underlying symplectic manifold with a locally constant sheaf of rings. When the fiber of this sheaf of rings is perfectoid of characteristic p, it is possible to specialize the Novikov parameter t = 1, and the Lagrangians in the resulting category can be matched with vector bundles on the equal-characteristic-version of the Fargues-Fontaine curve.
Don’t worry, it is just a story about triangles on a torus. The preprint is on arXiv and is probably more worthy of your time than this talk.
Joint work with David Treumann.