Harmonic Analysis on Lie Groups and Applications to Optical Communications

We will study how traditional Fourier Analysis becomes Harmonic Analysis when the underlying symmetry of a Lie Group is present. We will concentrate on representations and Fourier Series on compact Lie Groups including SO3 and SU2. The Harmonic Analysis of these groups can be applied to optical communications theory. In particular, we will use it to explain components of Soliton Geometry, Vortex Filaments and Quantum Optics.

Alexander Hiller

University of Technology Sydney

Alex Hiller is an undergraduate in a combined degree of Bachelor of Engineering/Bachelor of Science at the University of Technology Sydney (UTS) and is planning to graduate mid-2020. He has training in Electrical Engineering and the Biological Sciences but has developed a passion for Mathematics over the last few years, taking him beyond what is required by his engineering degree. Over the last year, Alex has also had significant involvement in the teaching of first-year mathematics, programming and physics. He has delivered tutorials for these subjects, generated lab materials and thoroughly enjoys communicating mathematical theory as well as approaches to doing calculations. His preferred programming language is C, he listens to podcasts daily, and currently he prefers to work with a fountain pen alongside a stack of blank, loose-leaf A4 paper.

Alex hopes to pursue a career in research, focused around mathematics. Some of his scientific heroes are John von Neumann, Richard Feynman, Robert Sapolsky, Eric Weinstein, Terence Tao and Grigori Perelman.

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