We derive and analyze an infinite-dimensional semidefinite program which computes least distortion embeddings of flat tori \(\mathbb {R}^n/L\) , where L is an n-dimensional lattice, into Hilbert spaces. This enables us to provide a constant factor improvement over the previously best lower bound on the minimal distortion of an embedding of an n-dimensional flat torus. As further applications we prove that every n-dimensional flat torus has a finite dimensional least distortion embedding, that the standard embedding of the standard torus is optimal, and we determine least distortion embeddings of all 2-dimensional flat tori.
