This all depends on your major and your advisors, of course, but...
- To find out whether you can contribute to MIRI's technical research at this time, you could apply to attend a workshop and/or write up some of your own comments on MIRI's published papers, like Quinn did.
- We explained what someone could do on IEM with Yudkowsky (2013) and Grace (2013). Katja has the most detailed picture of what exactly someone would do next, if you're interested. Some of the work would be CS-related (like Katja's report), some of it would be about evolutionary biology, some of it would be on other topics.
- For more sociological work, one could follow up on these two projects, which are both on "pause" right now. We outlined pretty clearly what the next steps there would be.
For you specifically, it seems you'd have to do something fairly technical. Is that right? If so, I can try to talk through which pieces of MIRI's technical research agenda you're most likely to be able to contribute to, if you tell me more about your background. E.g. which of the subjects here are you already familiar with?
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If you're not already familiar with Idris, I highly recommend checking it out -- it's a dependently typed Haskell variant, a bit like Agda but with a much friendlier type syntax. The downside of Idris is that, as a newer language, it doesn't have nearly as robust a standard library of proofs as, say, Coq. That said, the author, Edwin Brady, is keenly focused on making it a good language for expressing security properties in.
The field I work in has to do with proving that program errors related to maliciously crafted input cannot occur; if it'd be useful I'm happy to braindump/linkdump.
I'd heard of Idris. Parts of it sound really good (dependent typing, totality, a proper effects system, being usable from Vim), although I'm not a huge fan of tactic-based proofs (that's what the Curry-Howard Isomorphism is for!). It's definitely on the top of my list of languages to learn. I wasn't aware of the security focus, that is certainly interesting.
Proving safety in the face of malicious input sounds fascinating -- a dump would be much appreciated.