### Book chapter

## Topological recursion and Givental’s formalism: Spectral curves for Gromov-Witten theories

We describe a way of producing local spectral curves for arbitrary

semisimple cohomological field theories (and Gromov-Witten theories in par-

ticular) and global spectral curves for semisimple cohomological field theories

satisfying certain conditions. By this we mean that applying the topological

recursion procedure on the spectral curve reproduces the total potential of the

corresponding cohomological field theory.