Floer cohomology and Platonic solids

We consider Fano threefolds on which SL(2,C) acts with a dense

open orbit. This is a finite list of threefolds whose classification

follows from the classical work of Mukai-Umemura and Nakano. Inside

these threefolds, there sits a Lagrangian space form given as an orbit

of SU(2). We prove this Lagrangian is non-displaceable by Hamiltonian

isotopies via computing its Floer cohomology over a field of non-zero

characteristic. The computation depends on certain counts of holomorphic

disks with boundary on the Lagrangian, which we explicitly identify.

This is joint work in progress with Jonny Evans.