Talks

Constraint free initial data can be given for vacuum general relativity on a pair of intersecting null hypersurfaces. Moreover, the Poisson algebra of a set of such free null initial data has been found,but it has an unfamiliar structure, making its quantization difficult. We note that this algebra is essentially a sum of an infinite number of copies of the Poisson algebras of cylindrically symmetric gravity. Using the fact that cylindrically symmetric gravity is integrable we find new free data with an algebra more amenable to quantization.

I will report on progress understanding the 576-fold periodicity in TMF in terms of conformal field theoretic constructions.  Sporadic finite groups and their cohomology will play a role.

Bell's theorem shows that our intuitive understanding of causation must be overturned in light of quantum correlations. Nevertheless, quantum mechanics does not permit signalling and hence a notion of cause remains. Understanding this notion is not only important at a fundamental level, but also for technological applications such as key distribution and randomness expansion. It has recently been shown that a useful way to determine which classical causal structures give rise to a given set of correlations is to use entropy vectors. We consider the question of whether such vectors can lead to useful certificates of non-classicality. We find that for a family of causal structures that include the usual bipartite Bell structure they do not, in spite of the existence of non-classical correlations. Furthermore, we find that for many causal structures non-Shannon entropic inequalities give additional constraints on the sets of possible entropy vectors in the classical case. They hence lead to tighter approximations of the set of realisable entropy vectors, which enables a sharper distinction of different causal structures. Whether these improved characterisations are also valid for the quantum case remains an open problem whose resolution would have implications for the discrimination of classical and quantum causes.