I'm a mathematics student in my junior year and I'm interested in computational complexity and specially geometric complexity theory. I'm going to learn algebraic geometry and representation theory but I want to consider the parts that are related to geometric complexity theory so I wonder What are the topics that should be mastered by someone who wants to understand geometric computational complexity?
Surely, a lot of algebraic geometry and representation theory are needed, but which topics? and representation theory of what? finite groups? lie algebras(probably not) etc? and which topics in algebraic geometry are needed? It would be great if it is possible to name some topics that are required to be well understood in algebraic geometry and representation theory to before tackling geometric complexity theory. naming good resources ( texts etc ) that cover this background will be highly appreciated too.
I have asked the same question on math stackexchange but got no answer, so I thought I should ask it here.