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What topics/areas of algebraic geometry (aside from perverse sheaves/D-modules, etale cohomology, and possibly derived algebraic geometry) is it useful to learn/master if one is interested in doing research in geometric representation theory? What are the best sources to learn these topics? How does one know that one understands the material on a deep enough level to do interesting research?

My impression is that reading almost all of Hartshorne and solving a large portion of problems there (+ reading some specialized literature in geometric representation theory) is insufficient to solve interesting research problems. How different is preparation for research in geometric representation theory from preparation for research in other areas of algebraic geometry? Does one need a deep understanding of differential geometry and analysis and how to gain it, or are there specific areas/topics in geometry and analysis which are more useful to learn/understand?

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    $\begingroup$ What about symplectic geometry ? I think symplectic resolutions are really useful in geometric representation theory. $\endgroup$
    – Nicolas Hemelsoet
    Commented Jan 20, 2020 at 19:40
  • $\begingroup$ @Nicolas Hemelsoet But I think symplectic geometry is a really big/deep area with a lot of very analytic aspects, so what exactly should one learn from it? I've read Chriss and Ginzburg/Ginzburg's lectures on various subjects, they have symplectic geometry to some extent. What other things in symplectic geometry should one learn? $\endgroup$
    – Yellow Pig
    Commented Jan 20, 2020 at 19:45
  • $\begingroup$ I was thinking to what is described here : conferences.cirm-math.fr/1956.html $\endgroup$
    – Nicolas Hemelsoet
    Commented Jan 20, 2020 at 20:10
  • $\begingroup$ @Nicolas Hemelsoet Thanks a lot, I heard of this conference at Luminy, but it is all about very current research, not some reading background, right? Also, the link does not open when I press it $\endgroup$
    – Yellow Pig
    Commented Jan 20, 2020 at 20:17
  • $\begingroup$ I guess, you already had a look at the book of Chriss and Ginzburg? $\endgroup$
    – Lennart Meier
    Commented Jan 20, 2020 at 20:41

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