**Title: The Fargues-Fontaine curve for symplectic geometers**

**Abstract:**

Homological mirror symmetry describes Lagrangian Floer theory on a torus in terms of vector bundles on the Tate elliptic curve. A version of Lekili and Perutz’s works “over Z[[t]]”, where t is the Novikov parameter. I will review this story and describe a modified form of it, which is joint work with Lekili, where the Floer theory is altered by a locally constant sheaf of rings on the torus (an “F-field”). When the fiber of this sheaf of rings is perfectoid of characteristic p, and the holonomy around one of the circles in the torus is the pth power map, it is possible to specialize to t = 1, and the resulting theory there is described in terms of vector bundles on the equal-characteristic-version of the Fargues-Fontaine curve. I’m sorry about the title, I won’t assume that you’re a symplectic geometer, or that you ordered a Fargues-Fontaine curve.

Wednesday, February 27, 4:30 – 5:30 p.m.

Mathematics 520

Tea will be served at 4:00 p.m.