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Twistor analysis of a parabola

Presented by: 
Simon Salamon King's College London, Politecnico di Torino
Date: 
Tuesday 28th June 2016 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons