Abstract: In this talk, I will present a recent joint work with Yuexun Wang and Zhouping Xin establishing global existence and modified scattering for solutions to the modified Whitham equation with small, smooth, localized initial data. This work employs the space-time resonance method—a framework developed in recent years with numerous significant applications to long-time behavior of dispersive equations. The main difficulties arise from the slow decay and the non-homogeneity of the dispersion relation. We overcome these by introducing an interaction multiplier theorem and by estimating weighted norms in the frequency space. A key step is to extract certain good terms arising from integration by parts in time priori to the energy estimate so as to exploit the absence of time resonance effectively.