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We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, which generalizes the familiar probability tables used in non-locality theory to cover Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to *obstructions to the existence of global sections*. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. Some ongoing work with Shane Mansfield and Rui Soares Barbosa is described, which identifies *cohomological obstructions* to the existence of global sections, opening the possibility of applying the powerful methods of cohomology to non-locality and contextuality.

Cosmic strings are a generic prediction of Grand Unified Theories that can leave a sufficient imprint in the Cosmic Microwave Background anisotropies to open an observational window into an otherwise unreachable high energy domain. Being formed as topological defects of a Higgs field, they are also naturally coupled to various other fields, that can lead to superconducting-like currents, hence radically changing their structure and properties. After having summarized the standard string network behaviour and its cosmological effects, I will concentrate on the current-carrying properties and show how those can modify drastically the overall picture. In particular, I will exhibit the many current case, including the special non abelian situation that requires more care to be fully understood.

The fluid/gravity correspondence relates hydrodynamic flows in D spacetime dimensions to black hole dynamics in D+1 dimensions. It is an extension of black hole thermodynamics, where charges are upgraded into local currents, and the Bekenstein-Hawking entropy - into a local entropy current. I will propose a definition for a generalized local current of Wald entropy relevant to higher-curvature gravity. As an example, I will consider 5d gravity with a U(1) gauge field and a gravitational Chern-Simons term. This corresponds to a charged fluid in 4d spacetime, whose charge current has a gravitational anomaly. I will discuss the effects of this anomaly on the generalized entropy curent and the flow equations.

Relativistic quantum information theory uses well-known tools coming from quantum information and quantum optics to study quantum effects provoked by gravity and to learn information about the spacetime. One can take advantage of our knowledge about quantum optics and quantum information theory to analyse from a new perspective the effects produced by the gravitational interaction. I will present some results and new ideas in this topic: from experimental proposals for detection of the Unruh and Hawking effects and cosmological implications of gravitationally generated entanglement to quantum simulation of general relativistic settings.

The history of physics, from Galileo's spatialization of time to Einstein's block universe, and on to Julian Barbour's timeless quantum cosmology, tells a story by which time is demoted from a fundamental aspect of experience to an emergent illusion in a world held to be fundamentally timeless. The question I would like to address is, is this correct, or will the next stage in the development of physics require a rediscovery of time as a primary aspect of nature? One reason to bet on the reality of time is the strength of the argument of Pierce that laws of nature require explanation and that laws must evolve to be explained. This implies that time is prior to law, which means time cannot emerge from timeless law. This however raises a problem: is the evolution of law lawful? Are all laws effective and approximate? Is there a metalaw which governs the evolution of laws? If so, what selects the metalaw? One approach to this meta-laws dilemma is that the distinction between dynamical laws and the states they act on, which is absolute in most physical theories, is emergent. I present a simple model to illustrate this approach. This talk is partly based on joint work with Roberto Mangabeira Unger.

In his article `More is Different', P W Anderson (1972) sensitized the physics community about importance of emergence, by using concepts such as broken symmetry, emergent hierarchical structures, constructionists converse of reductionism etc. The manifestation of complexity and hierarchy in the quantum many particle systems go beyond broken symmetries. In certain quantum systems we have the opposite - emergence of new local gauge symmetries. This idea was introduced, for example, for Mott insulators, by Anderson and us in 1988. Properties such as entanglement, different possible statistics of identical particles, multi particle wave interference, vastness of Hilbert space etc;, which are unique to the world of quantum, leads to a wonderful richness in physics and mathematics, including emergent gauge symmetries, gauge fields, quantum order, holographic correspondences and continuing surprises.