## Topological string theory

### Dr. Alessandro Tanzini

Prerequisites: classical mechanics, differential geometry.

Contents:

- First part:
- Equivariant cohomology and Localisation Formulae (Duistermaat-Heckman and Atiyah-Bott). Mathai-Quillen formalism for the Euler class of vector bundles.
- Field theory in zero dimensions: a toy model of Supersymmetry.
- Euler class of infinite dimensional vector bundles (Atiyah-Jeffrey).
- Path Integral formulation of Quantum Mechanics: Feynman-Kac formula.
- Supersymmetric quantum mechanics as the regularized Euler number of loop space.
- Supersymmetric Quantum Mechanics and Morse theory. Morse inequalities and Morse-Witten complex.

- Second part:
- Supersymmetry algebra in two dimensions. Topological twist: A model and B model.
- Mathai-Quillen formalism for Gromov-Witten invariants.
- Brief introduction to mirror symmetry.