"A new spinfoam vertex" probably MIP for second quarter The new paper of Livine and Speziale could very well turn out to be the most influential paper of second quarter 2007. http://arxiv.org/abs/0705.0674 A new spinfoam vertex for quantum gravity A large part (perhaps majority) of research effort in non-string QG is focused on the spinfoam approach. this is a path integral, or sum-over-histories approach-----the spinfoam is a 4D spacetime path linking two spinnetwork quantum states of geometry, a "before" state and an "after" state. Each spinfoam is a way that one state can evolve into another, and for each such spinfoam "evolutionary pathway" it must be possible to compute an AMPLITUDE. One should be able to sum or average-----to integrate over all these spinfoams---to get the overall amplitude of one particular state evolving into another. the amplitude of a spinfoam is computed by evaluating a vertex function of the data at each vertex. Also every spinfoam has a dual where each 4D simplex is replaced by a vertex and vice versa, do I suppose one can think of the vertex function being evaluated on each simplex of the dual: block by block. until now much of the spinfoam research effort has focused on the BARRETT-CRANE model, where one uses a particular BC vertex function. The BC model has attractive features---as explained in this paper, among others---but also one or more drawbacks, which Livine and Speziale mention as well. It seems to me that what Livine and Speziale are proposing to do is break a potential log-jam in spinfoam research by offering a NEW vertex function---call it the "LS model" or the "LS vertex"---which will not have these drawbacks. Two reasons I like their paper are (1) it is clearly written (they put care into making it understandable) and (2) they have been doing numerical work---such as computer simulations---in parallel with their theoretical progress. Each theory step they take, they try it out and support it with numerical work.