Feynman graph integrals from topological holomorphic theories

Feynman graph integrals from topological theories were developed by M. Kontsevich, S. Axelrod and I. M. Singer in 1990s. These integrals have many mathematical applications, such as knot invariants, operad theory and formality theorems. In this talk, I will talk about Feynman graph integrals from topological-holomorphic theories. In particular, I will prove the finiteness of Feynman graph integrals when spacetime is flat spaces and a vanishing result of graph integrals. Combining the vanishing result with Batalin-Vilkovisky(BV) formalism, we can show the absence of anomalies of topological-holomorphic theories on flat spaces with at least two topological dimensions. As a consequence, we can construct factorization algebras of quantum observables. This is joint with Brian Williams.