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The "Lefschetz thimble" and the sign problem
In this talk I illustrate an approach the we recently proposed to perform Monte Carlo simulations of lattice field theories with a sign problem. The approach consists in formulating the theory on a "Lefschetz thimble" (that will be introduced). The new formulation does not coincide with the original one exactly, but it can be justified in terms of symmetries and perturbation theory, and hence on the basis of universality. I also illustrate the Aurora algorithm that we proposed to sample the configurations from the thimble. Finally I show the results of our first numerical tests on small lattices and applied to a simple model. These results are very encouraging in view the wide applicability - in principle - of our approach.