Search for $D^0\to\gamma\gamma$ and improved measurement of the branching fraction for $D^0 \to \pi^0\pi^0$

Using 2.92 fb(-1) of electron-positron annihilation data collected at root s = 3.773 GeV with the BESIII detector, we report the results of a search for the flavor-changing neutral current process D-0 -> gamma gamma using a double-tag technique. We find no signal and set an upper limit at 90% confidence level for the branching fraction of B(D-0 -> gamma gamma pi(0)pi(0)) = (8.24 +/- 0.21(stat) +/- 0.30(syst)) x 10(-4), the most precise measurement to date and consistent with the current world average.