Anders Yu
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).
Anders Yu
The University of Adelaide
Anders Yu is a third-year Bachelor of Mathematical Sciences (Advanced) student at the University of Adelaide, majoring in Pure Mathematics. They intend on pursuing research in academia after completing their undergraduate studies, and are currently interested in differential geometry and algebraic topology. Anders is fascinated by pure mathematicians’ ability to imagine and make connections between abstract mathematical ideas through rigorous proof and reasoning.
You may be interested in
Bradley Landau
How do phase transitions emerge in discrete vector-spin generalisations of the Curie–Weiss model?