Notes on (twisted) lattice supersymmetry

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We describe a new approach to the problem of putting supersymmetric theories on the lattice. The basic idea is to discretize a {\it twisted} formulation of the supersymmetric theory. For certain theories with extended supersymmetry these twisted formulations contain only integer spin fields. The twisting exposes a scalar nilpotent supercharge which generates an exact lattice symmetry. We gives examples from quantum mechanics, sigma models and Yang-Mills theories.
Summary of lectures given at the Summer Institute 2005 Fuji-Yoshida, Japan August 11-18, 2005

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