This page collects notes, study resources, and problem solutions as I learn twistor theory. Advanced topics get sparse fast: few textbooks, scattered lecture notes. etc. So I’m filing my own trail here in the hope it helps others, and to track my own learning.
Prerequisites: solid differential geometry; special relativity (lightcones, index gymnastics); some complex geometry; a foundational grasp of algebraic geometry. Background in QFT, and perhaps string theory, helps.
We start with a zoomed-out view: what is it twistor theory seeks to explain? We can then understand why null geometry should be centre stage.
Review of special relativity with an emphasis on lightcones, null directions, and conformal compactification.
Weyl spinors, the $SL(2,\mathbb{C})$ double cover, abstract index notation, and the spinor–helicity toolkit.
The definition of twistor space, the correspondence between spacetime points and lines in twistor space, and the incidence relation.