A student who specialises in algebraic geometry has contacted me to ask if they could collaborate with me on some problem which relates mathematical physics and algebraic geometry. I think his idea is that he knows more about algebraic geometry and I know more about physics and QFT, so he is asking if there is some problem which combines both where we would both contribute decisively.

I would be keen to stay away from string theory for now if possible, so I was wondering if there is some interesting research problem at the moment which combined both QFT and algebraic geometry (I can be more specific about the type of algebraic geometry which he does if necessary if the problem needs to be narrowed down further).