Abstract:
I will prove finite generatedness properties for several semi-simplecohomological field theories obtained from Gromov-Witten theories. I will alsoexplain the generalisation of finite generatedness to relative settings. Afterthat, I will give several applications. The first is holomorphic anomalyequation for local P2 and formal quintic invariants and the second is crepantresolution correspondence for C3/Z3. Lastly, I will prove some tautological relations on the moduli space ofstable maps to X. First part of this talk is based on the joint work with RahulPandharipande and last part is based on the joint work in progress withYounghan Bae.