Visualising complex functions: Enhanced phase portraits

Abstract: Complex functions are essential mathematical objects in complex analysis. They play a fundamental role in other mathematical areas such as dynamics, algebraic and differential geometry, and number theory; and advanced theoretical physics such as quantum mechanics, string theory, and quantum field theory. Visualising complex functions is a non-trivial task since they will produce a graph existing in a four-dimensional space. In this presentation, we provide an overview of the method known as domain colouring to visualise and explore complex functions. We also present a set of open-source online tools which main goal is to help students, and anybody interested in this topic, to create significant connections between visual representations, algebraic calculations and abstract mathematical concepts about complex functions.

The recording from this seminar is currently unavailable, sorry.

Additional links:

• Presentation slides
• Online tools for domain colouring: https://www.dynamicmath.xyz/domain-coloring/
• Mobius transformations: https://www-users.cse.umn.edu/~arnold/moebius/
• Course page: https://courses.smp.uq.edu.au/MATH3401/Lectures.html