Wave packet decompositions and sharp bilinear estimates for rough Hamiltonian flows

Wave packet parametrices decompose dispersive evolutions into non-oscillating components. Presently, we obtain refined wave packet parametrices for dispersive equations with low-regularity coefficients. The required pointwise regularity is sharp. We use the parametrices to extend sharp bilinear Fourier extension estimates due to Wolff and Tao to those evolutions.

Based on joint work with Daniel Tataru (UC Berkeley).