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Penrose Transform

Geometrical Langlands Correspondences (Cycles and Co-cycles)

Geometrical Picture

1

Penrose-Radon Transform

Orbifolds

CY-Manifolds

2

Penrose-Ward Transforma

Hyper-plane Twistor Space

3

Classic Penrose Transform

Celestial Spheres

4

Penrose-Schmid Transform

Dimensional complex

Sub-manifolds

5

Classic Penrose Transform

Space-Time (Minkowski Space)

5

Radon Transform

Hyperbolic Disk