Effective Batalin-Vilkovisky quantization and geometric applications

Understand

We explain the effective renormalization method of quantum field theory in the Batalin-Vilkovisky formalism and illustrate its mathematical applications by three geometric examples: (1) Topological quantum mechanics and algebraic index, (2) Elliptic curve and higher genus mirror symmetry, (3) Calabi-Yau geometry and integrable hierarchy.

• This note is an expansion of author's talk at ICCM 2016.