I'm interested in studying algebraic analysis, specifically the area described in here https://en.wikipedia.org/wiki/Algebraic_analysis and also the theory of D-modules, as I find the idea of "doing analysis with algebra" quite attractive and also because it seems like a very rich field in terms of the present underlying interactions between various fields in mathematics. I'm a graduate student, having covered the basics of Smooth Manifolds, Commutative Algebra, some Algebraic Geometry, some Functional Analysis, and also quite a bit of Complex Analysis in one variable. I'm wondering about:
- What are the prerequesites to study algebraic analysis and what is recommended to be comfortable with when getting into it?
I'm guessing I'll need to know a lot of Geometry, e.g. Symplectic Geometry, Complex manifolds, Algebraic Geometry and a lot of Category theory and Sheaf theory. I'm not sure if there's more I need to study from functional analysis and PDE's as well. I would like to know the prerequesites so that I can have a clear path to get to algebraic analysis.
All comments and answers are appreciated and I thank you in advance :)
