An introduction to the superspace formalism

Supersymmetry is an extension of the Poincaré symmetry - the isometries of flat space, a very geometric object - by some number of odd generators. It is then natural to expect that supersymmetry also has a geometric interpretation. In particular, can supersymmetry arise as the isometries of some manifold? Unsurprisingly, the answer turns out to be yes, but only in very special cases. In this talk, I will introduce two-dimensional $\mathcal N$=(2,2) supersymmetry as the isometry algebra of a manifold called $\mathcal N$=(2,2) superspace, and we shall see how far we can push this formalism within the constraints of the clock.