I have been studying topological quantum field theory by mainly reading the Turaev's book.

I'd like to know if there are unsolved problems that motivate mathematicians to study TQFT, like Riemann's hypothesis for number theory.

I also would like to know if there is a paper or book that list big or small unsolved problems of TQFT. If not, could you suggest some problems here? I have been learning TQFT but I don't know what to do by myself as a graduate student.

Thank you.