Michael Goldberg (U. Cincinnati) Pointwise bounds for the 3dimensional wave equation and spectral multipliers Abstract: The sine propagator for the wave equation in three dimensions, $\frac{\sin(t\sqrt{\Delta})}{\sqrt{\Delta}}$, has an integral kernel $K(t,x,y)$ with the property $\int_{\mathbb R} K(t, x, y)dt = (2\pixy)^{1}$. Finiteness comes from the sharp Huygens principle and powerlaw decay comes from dispersion. Estimates of this type are useful for proving ``reversed Strichartz" inequalities that bound a solution in $L^p_x L^q_t$ for admissible pairs $(p,q)$. We examine the propagator $\frac{\sin(t\sqrt{H})}{\sqrt{H}}P_{ac}(H)$ for operators $H = \Delta + V$ with the potential $V$ belonging to the Katonorm closure of test functions. Assuming zero is not an eigenvalue or resonance, the bound $\int_{\mathbb R} K(t,x,y) \leq Cxy^{1}$ continues to be true. Combined with a Huygens principle for the perturbed wave equation, this estimate suggests pointwise bounds for spectral multipliers of fractional integral or H\"ormanderMikhlin type. This is joint work with Marius Beceanu (SUNY  Albany). 
