Kevin Costello

The B model partition function and the holomorphic anomaly equation.

If X is a Calabi-Yau, the B model partition function is a state in the Fock space of the symplectic vector space H*(X)((t)). The holmorphic anomaly equation tells us how this behaves when we vary the complex structure on X : the partition function is flat for a certain natural connection on the Fock space. I'll discuss some aspects of the construction of the partition function and the proof of the holomorphic anomaly.