Computational Topology with Benjamin Burton and Rhuaidi Burke

Today, we have an exciting episode at the intersection of computer science and mathematics! Ben Burton and Rhuaidi Burke, from the School of Mathematics and Physics at UQ, both work in the field of computational topology. They’re here to give a brief introduction to computational topology, as well as some of the unique challenges that arise when writing software for mathematicians.

Benjamin Burton (pronouns he/him) is a professor in the School of Mathematics and Physics at The University of Queensland, where he spends his time teaching supercomputers how to untangle knots. His mathematical career has spanned geometry, cryptography and finance, and he enjoys puzzling over how to find fast computational solutions to difficult mathematical problems. Benjamin is passionate about bringing mathematics to the public, and he has worked behind the scenes for many years to help organise the International Olympiad in Informatics and other secondary outreach programmes. He also volunteers for the Debian GNU/Linux project, and knows more about Eurovision than you will ever need to know.

Rhuaidi Burke is a PhD student working on 4-dimensional computational topology. Specifically, he is investigating combinatorial representations of "exotic" 4-dimensional spaces — these are spaces which can be continuously deformed into one another, but not smoothly deformed into one another — a phenomenon which only appears in dimensions 4 and higher.

Some links:

• Regina: https://regina-normal.github.io/
• SnapPy: https://snappy.math.uic.edu/
• Curved Spaces, “a flight simulator for multi-connected universes”: https://www.geometrygames.org/CurvedSpaces/index.html
• The Shape of Space by Jeffrey R. Weeks: https://www.routledge.com/The-Shape-of-Space/Weeks-Weeks/p/book/9781138061217
• The four colour theorem: https://en.wikipedia.org/wiki/Four_color_theorem
• Persistent homology: https://en.wikipedia.org/wiki/Persistent_homology
• Jeff Erickson’s course on computational topology at Illinois: http://jeffe.cs.illinois.edu/teaching/compgeom/