Programme Speaker: Prof. Dan Christensen Title: Finiteness and Positivity for the Lorentzian partition function Abstract: This talk gives an overview of recent results on the Lorentzian Barrett-Crane model, a spin foam model of quantum gravity. I will begin with a concise proof of the finiteness of the Lorentzian 10j symbol, which generalizes to other integral expressions of the same form, such as causal models. I then describe work of my student Wade Cherrington which uses the generalized finiteness result above to show that the Lorentzian partition function for a fixed triangulation is finite in the Perez-Rovelli normalization. Finally I will outline joint work with Cherrington which shows that the Lorentzian partition function is non-negative. In fact, we show that the Lorentzian Barrett-Crane model can be reformulated as a model with non-negative amplitudes, and this leads to the possibility of efficient computations of expectation values using statistical methods. Talk: Transparencies, Recorded Talk