3 problems

Gaussian absolute-continuity conjecture. If $4\mu$ is a suitable Gaussian measure on $h^{s+\frac{1}{2}}$, then the corresponding measure $4\rho_s$ is absolutely continuous with res…

Local Birkhoff coordinates conjecture. There exist an open neighborhood $U$ of $\varphi_c$ in $iL^2_r$, an open neighborhood $V$ of zero in…

For the KdV equation, let $\Psi$ denote a Birkhoff map and let $\Psi_0$ be its linearization at the equilibrium point $q=0$. A map is 1-smoothing when its nonlinear part has the sm…