All 4d toric Kahler geometries with CKY 2-form

Kahler geometries admitting additional twistor structures, like CKY forms, are of interest to mathematical physics due to their intrinsic relation to integrability and separability of PDEs emerging, for example, in supergravities and string theory. In this talk I will present an explicit classification of all local 4d Kahler metrics with toric symmetry admitting a CKY 2-form. We will also discuss the generalisation of this result for non-toric geometries.