## Topological Field Theory

### Alessandro Tanzini

- Part 1: from classical mechanics to supersymmetry
- review of classical mechanics (Hamilton, Lagrange, Hamilton Jacobi formulations)
- classical field theory: Noether theorem, scalar fields and sigma models, Clifford algebrae and spinor fields, gauge fields, instantons, monopoles
- supersymmetry: supermanifolds, superfields, supersymmetric sigma models, gauge theories with (extended) supersymmetry

- Part 2: path integral representation of topological invariants
- path integral formulation of quantum mechanics, Feynman-Kac formula. Gauge fields and BRS symmetry.
- topological quantum field theories: supersymmetric quantum mechanics and the Euler characteristic, topological sigma model and Gromov-Witten invariants, Chern-Simons theory and knot invariants, [BF theory and Batalin-Vilkoviski formalism], topological Yang-Mills theory and Donaldson invariants.