On 26 April 2023 I gave a talk in the Monash topology seminar.

**Title:** Spinors and horospheres

**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 in terms of Minkowski space. We present some extensions of this work, involving 3-dimensional hyperbolic geometry. In particular, we give a correspondence between between nonzero pairs of complex numbers, called spin vectors, and horospheres in 3-dimensional hyperbolic space decorated with certain spinorial directions. We show that the natural inner product on spin vectors describes a certain complex-valued distance between decorated horospheres, generalising Penner’s lambda lengths, and giving various applications.

Slides from the talk are below.

23-04-26_Monash_talk_slides