A "spin foam" is a higher-dimensional analogue of a Feynman diagram where instead of a graph we use a higher-dimensional complex with vertices, edges and faces. Loop quantum gravity gives an interesting picture of the quantum geometry of space, and spin foam models seek to supplement this with a picture of the quantum geometry of spacetime. Here we summarize results of both analytical work and extensive computer calculations in two spin foam models: the Barrett-Crane models of Riemannian and Lorentzian quantum gravity in 3+1 dimensions.
You can see the slides here:
For more on this subject try these papers:
You can also see photos of the conference where I gave this talk!
I also wrote an issue of This Week's Finds about this conference: week206.