Nyx Crosby
The Hopf Fibration
The Hopf fibration is a particular map from a three-dimensional sphere to a two-dimensional sphere with a variety of interesting properties. It is one of the simplest examples of a non-trivial principal bundle, an object which is of great importance in differential geometry and physics. The Hopf fibration is a fundamental example in homotopy theory, and has connections to the theory of Lie groups, spin geometry, quaternions, and projective spaces. There are various ways in which it can be generalised. The goal of this project is to understand the many interesting algebraic and geometric features of the Hopf fibration without relying on advanced machinery (e.g. differential geometry).
Nyx Crosby
The University of Adelaide
Nyx Crosby is a hard-working and passionate student at the University of Adelaide. She is an undergraduate student studying a Bachelor of Science, with a major of Theoretical Physics, and a Bachelor of Mathematical Sciences, with a major of Pure Mathematics. She is especially interested in the intersection of pure maths and theoretical physics, which she aims to pursue in an academic career in maths. Outside of study, Nyx spends a lot of her time reading books and playing board games.
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