Ryan Buchanan and Andrius Kulikauskas investigate
How can we generate all minimally nontrivial systems?
This includes: What are some of the "nicest" non-trivial spaces?
Examples of minimally nontrivial systems
- The Dynkin diagram of the Lie group {$SU(2)$} is given by a single dot. The trivial version would be the circle group {$SU(1)$}. The next nontrivial version would be {$SU(3)$}, whose Dynkin diagram is given by two dots linked by a line (which means the dots are simple roots separated by 120 degrees). After that you get chains of dots, and then after that you can add a widget at the end in four different ways. And that's basically it.
- See the video that Andrius made: 120°+120°=90° in Dynkin Diagrams. Teamwork in Creating Learning Paths. (What is Geometry?)