Global well-posedness of the Boltzmann equation via bilinear estimates

We prove global well-posedness of the hard-sphere Boltzmann equation in ${\mathbb{R}}^d$ for small initial data in the critical Besov space $B_{1,1}^{d-1}{L}_v^1$ and in the critical Sobolev space $W^{d-1,1}{L}_v^1$. The proof is based on new bilinear estimates for the nonlinear collision operator, which rely on transversality considerations.