Talks

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.

The fundamental constants of our universe may have been set to maximize the production of similar universes, through repeated parametric variation. In this context, I will advocate that by the time the maximum entropy producer in our universe has reached maximum complexity, the majority of its energy should be re-purposed towards the production of additional universes. This builds on elements of prior proposals, including cosmological natural selection, the nonsingular universe, and the causal entropic principle. The phenomena and properties of dark matter, which realizes this proposal by copious conversion of halo baryons to black holes in ten trillion years, will be discussed.

If we want a mechanism for the current cosmic expansion that is alternative to (and possibly more “natural” than) the cosmological constant, there exist intriguing proposals within the dark energy and modified gravity realm.

First, I will briefly review the status of one of the most promising ideas, massive gravity: cosmological solutions, some formal aspects and recent developments. Then, I will present recent work aimed at constraining such models with LSS probes.