Exact Results in Quantum Theory

The dynamics of loop quantum gravity can be studied in a covariant way using the spin foam formalism, which provides a path integral for spin networks. The most successful spin foam model so far is the EPRL model, and its generalization studied in Warsaw. In my talk, I will discuss how these amplitudes represent histories of discrete geometries. In particular, I will present a new and elegant derivation of the amplitude in terms of twistors, and discuss some of its semiclassical properties.