ABSU will be performing at the Hammer Open Air Festival in Lieto, Finland on July 15th, 2011. I haven't heard if they will be performing any new songs but it's very possible. In the meantime, they are preparing to master the new album "Abzu" which does not yet have a definitive release date but will likely be out in October according to Ezezu.
In the meantime, an official new website will be under construction soon as well as an official Facebook page, and Soundcloud page. Thanks for your patience!
Until then, Equitant has released a new track for his upcoming album. You can hear it here.