A C0C^0-estimate for the parabolic Monge-Amp\`{e}re equation on complete non-compact K\"ahler manifolds

In this article we study the K\"ahler Ricci flow, the corresponding parabolic Monge Amp\`{e}re equation and complete non-compact K\"ahler Ricci flat manifolds. In our main result Theorem \ref{mainthm} we prove that if $(M, g)$ is sufficiently close to being K\"ahler Ricci flat in a suitable sense, then the K\"ahler Ricci flow \eqref{KRF} has a long time smooth solution $g(t)$ converging smoothly uniformly on compact sets to a complete K\"ahler Ricci flat metric on $M$. The main step is to obtain a uniform $C^0$-estimates for the corresponding parabolic Monge Amp\`{e}re equation. Our results on this can be viewed as a parabolic version of the main results in \cite{TY3} on the elliptic Monge Amp\`{e}re equation

The SETI episode in the 1967 discovery of pulsars

In the winter of 1967 Cambridge radio astronomers discovered a new type of radio source of such an artificial seeming nature that for a few weeks some members of the group had to seriously consider whether they had discovered an extraterrestrial intelligence. Although their investigations lead them to a natural explanation (they had discovered pulsars), they had discussed the implications if it was indeed an artificial source: how to verify such a conclusion and how to announce it, and whether such a discovery might be dangerous. In this they presaged many of the components of the SETI Detection Protocols and the proposed Reply Protocols which have been used to guide the responses of groups dealing with the detection of an extraterrestrial intelligence. These Protocols were only established some twenty five years later in the 1990s and 2000s. Using contemporary and near-contemporary documentation and later recollections, this paper discusses in detail what happened that winter.Comment: 18 pages. Published in The European Physical Journal: Historical Perspectives on Contemporary Physics, February 201