Re:Visual Group Theory: What is a group? (2016) [video]
by seppel on Saturday February 10, 2018 @11:51AM
(#16348090)
> In fact I am struggling to think of an application of groups to mathematics where geometry does not come into play.
Number theory is another example, finding roots of polynomials was already mentioned.
> Even the abstract classification of finite simple groups uses ideas from geometry on a very crucial way (representation theory).
It connects linera algera to group theory, yes. But representation theory is by far the least "visual" branch of group theory I can think of. It is on a similar "abstract nonsense" level as category theory (and I don't mean that in a bad way, it is just how things are). The only visualizations I can find in my representation theory scripts are commutative diagrams between group homomorphisms, vector space homomorphims and some module endomorphisms and what not :)
Number theory is another example, finding roots of polynomials was already mentioned.
> Even the abstract classification of finite simple groups uses ideas from geometry on a very crucial way (representation theory).
It connects linera algera to group theory, yes. But representation theory is by far the least "visual" branch of group theory I can think of. It is on a similar "abstract nonsense" level as category theory (and I don't mean that in a bad way, it is just how things are). The only visualizations I can find in my representation theory scripts are commutative diagrams between group homomorphisms, vector space homomorphims and some module endomorphisms and what not :)