James Grant attended the Central European Relativity Seminar III in Golm, Germany for 7-9 February.  His talk was titled “On differentiability of volume time functions“.   In the talk he showed differentiability of a class of Geroch’s volume functions on globally hyperbolic manifolds. Furthermore, it was proved that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally anti-Lipschitz can be uniformly approximated by smooth time functions with timelike gradient.  Finally, it was proved that in stably causal spacetimes Hawking’s time function can be uniformly approximated by smooth time functions with timelike gradient.  The presentation was based on joint work with P.T. Chrusciel and E. Minguzzi.  The website for the conference is here.