Twistor analysis of a parabola

Duration: 1 hour 4 mins

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Description:	Salamon, S (King's College London, Politecnico di Torino) Tuesday 28th June 2016 - 14:30 to 15:30


Created:	2016-07-06 11:36
Collection:	Gravity, Twistors and Amplitudes
Publisher:	Isaac Newton Institute
Copyright:	Salamon, S
Language:	eng (English)


Abstract:	The Penrose twistor space CP^3 can be used to parametrize orthogonal complex structures on domains of R^4. In particular, a complex quadric Q defines a natural complex structure on R^4 minus a line. Quaternionic power series can then be lifted to holomorphic maps from Q to CP^3. Applying this to a quadratic polynomial allows one to understand the elementary geometry associated to a parabola and the circular cones in 3-dimensional space that contain it.

Abstract:

The Penrose twistor space CP^3 can be used to parametrize orthogonal complex structures on domains of R^4. In particular, a complex quadric Q defines a natural complex structure on R^4 minus a line. Quaternionic power series can then be lifted to holomorphic maps from Q to CP^3. Applying this to a quadratic polynomial allows one to understand the elementary geometry associated to a parabola and the circular cones in 3-dimensional space that contain it.

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