The things you directly need are algorithmic complexity theory (Classic textbook: Li and Vitanyi) and some way of understanding proofs (Probably start with regular mathematical logic / model theory, not sure of a standout textbook here, maybe Manin?, then look into modal logic, classic textbook by Boolos).
Prerequisites for those are mathematical logic, set theory, probability theory, and some amount of discrete math.
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I'll be there too. Can't wait :)