Mathematical Physics Sector

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SISSA — International School for Advanced Studies Phonebook Webmail Library catalogue

Via Bonomea 265 — 34136 Trieste — Italy 45.679538°N, 13.774999°E

Topological string theory

Dr. Alessandro Tanzini

Prerequisites: classical mechanics, differential geometry.

Contents:

• First part:
  1. Equivariant cohomology and Localisation Formulae (Duistermaat-Heckman and Atiyah-Bott). Mathai-Quillen formalism for the Euler class of vector bundles.
  2. Field theory in zero dimensions: a toy model of Supersymmetry.
  3. Euler class of infinite dimensional vector bundles (Atiyah-Jeffrey).
  4. Path Integral formulation of Quantum Mechanics: Feynman-Kac formula.
  5. Supersymmetric quantum mechanics as the regularized Euler number of loop space.
  6. Supersymmetric Quantum Mechanics and Morse theory. Morse inequalities and Morse-Witten complex.
• Second part:
  1. Supersymmetry algebra in two dimensions. Topological twist: A model and B model.
  2. Mathai-Quillen formalism for Gromov-Witten invariants.
  3. Brief introduction to mirror symmetry.