An L${}^3$ bound for the trilinear Hilbert transform

We prove that the trilinear Hilbert transform with fixed slopes 1, 2, 3 maps $L^3(\mathbb{R})\times L^3(\mathbb{R})\times L^3(\mathbb{R})$ to $L^1(\mathbb{R})$, resolving this case of the trilinear Hilbert transform conjecture.