Recent Results On The Modulated Cubic Nonlinear Schrödinger Equation On ${\mathbb{T}}^2$

New Strichartz estimates for the modulated cubic nonlinear Schrödinger equation are proved. These Strichartz estimates allow us to show that this equation is pathwise locally well-posed. We also show that improved Strichartz estimates are available in the case where the modulation is white noise. Additionally, we comment on a few basic properties of the modulated cubic nonlinear Schrödinger equation such as conservation of mass and convergence of its linear flow as time tends to zero.