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69 votes
20 answers
19k views

Fun applications of representations of finite groups

Are there some fun applications of the theory of representations of finite groups? I would like to have some examples that could be explained to a student who knows what is a finite group but does not ...
21 votes
3 answers
7k views

What are the current breakthroughs of Geometric Complexity Theory?

I've read from Wikipedia about Geometric Complexity Theory (GCT) which (if I understood correctly) is a program for coping with the $ P=NP $ problem using algebraic methods. That program seems ...
14 votes
8 answers
2k views

Applications of the idea of deformation in algebraic geometry and other areas?

The idea of proving something by deforming the general case to some special cases is very powerful. For example, one can prove certain equalities by regarding both sides as functions/sheaves, and show ...
9 votes
1 answer
506 views

Current state of the art in geometric complexity theory

I came across this interesting question from almost 7 years ago: What are the current breakthroughs of Geometric Complexity Theory? My question is quite simple: Have there been any breakthroughs in ...
Bobby-John Wilson's user avatar