On 9 December 2024 I gave a talk in the Topology, Geometry and Dynamics seminar at the National University of Singapore.
Title: Spinors and lambda lengths
Abstract: Work of Penrose and Rindler in the 1980s developed a formalism for spinors in relativity theory. In their work they gave geometric interpretations of 2-component spinors as flags in Minkowski space. We present some extensions of this work involving hyperbolic geometry. In particular, we give a correspondence between between spinors and horospheres with certain decorations, and show how spinors can be used to calculate a complex-valued, 3-dimensional generalisation of Penner’s lambda lengths. Time permitting, we may discuss some further applications, including inter-cusp distances in knot complements, higher-dimensional generalisations, and circle packings.
Slides from the talk are below.
Spinors_and_lambda_lengths_24-12-09_for_web