Hypercomplex Numbers: How to I stopped worrying and learned to love multilinear algebra

Abstract: This seminar will serve up a smorgasbord of ideas revolving around the notion of hypercomplex numbers. Traditionally, the term hypercomplex number refers to an element of a finite-dimensional unital algebra over the field of real numbers. The hypercomplex numbers are stepping stones to learning about Lie groups and group representation theory.

My aim is to reframe some of the key underlying ideas in more modern mathematical language by using multilinear algebra and string diagrams as graphical notation, while simultaneously keeping intact the original intuition of generalizing complex numbers. Ultimately, I hope to motivate further exploration by showing several practical applications of hypercomplex numbers in computer graphics and data visualization.

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The talk will be moderated by Edmund Harriss. Edmund Harriss is a mathematician, artist, and assistant professor at the University of Arkansas. He is the discoverer of the Harriss spiral and the creator of the construction toy Curvahedra. He is the coauthor of Hello Numbers, What Can You Do? and the coauthor and illustrator of two mathematical coloring books: Patterns of the Universe and Visions of the Universe.

Computer scienceMathematics

Audience: researchers in the topic

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Relatorium seminar

Series comments: The name "Relatorium" combines "relator" with the Latin root "-ium," meaning "a place for activities" (as in "auditorium" or "gymnasium"). This seminar series is a platform to relate ideas, interact with math, and connect with each other.

In this series, we explore math beyond what we usually hear in standard talks. These sessions fall somewhere between a technical talk and a podcast: moderately formal, yet conversational. The philosophy behind the series is that math is best learned by active participation rather than passive listening. Our aim is to “engage and involve,” inviting everyone to think actively with the speaker. The concepts are accessible, exploratory, and intended to spark questions and discussions.

The idea of relatability has strong ties to compassion — creating space for shared understanding and exploration - which is the spirit of this seminar! This is a pilot project, so we’re here to improvise, learn, and evolve as we go!

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