**Abhay Ashtekar,** Pennsylvania State University

*Implications of the Quantum Nature Space-time for the Big Bang and Black Holes*

**Dorothea Bahns**, University of Goettingen

*Quantum Sine-Gordon model in perturbative AQFT*

We construct the Haag Kaster net of von Neumann algebras for the Sine-Gordon model. This is joint work with Klaus Fredenhagen and Kasia Rejzner.

**Beatrice Bonga**, Perimeter Institute

*Angular momentum flux in Einstein-Maxwell theory*

There are three natural currents for Maxwell theory on a non-dynamical background: the stress, Noether and canonical current. Their associated fluxes across null infinity differ by boundary terms for asymptotically flat spacetimes. These boundary terms do not only quantitatively change the behavior of the flux associated with an asymptotic Lorentz symmetry, but also qualitatively: the stress flux contains both radiative and Coulombic information, whereas Noether and canonical ones are purely radiative.

While all methods are equally valid and have their own range of usefulness, it is reasonable to ask if one definition is more natural than the other. In order to answer this question, we turn to general relativity. With Maxwell theory coupled to gravity, we use the Wald-Zoupas formalism to obtain an expression for the flux of angular momentum and find that it is purely radiative. When the gravitational field is ``frozen'', the Wald-Zoupas flux reduces to the Noether flux.

**Steven Carlip**, University of California, Davis

*Spacetime Foam and the Cosmological Constant*

I describe a radical proposal for the cosmological constant problem: perhaps Lambda really is very large, but is "hidden" in Planck-scale fluctuations of geometry and topology. I show that an enormous set of initial data describe a universe with such a hidden cosmological constant at an initial time. The question of whether this structure is preserved under time evolution is still open, but I provide some evidence that it may be. I close with a discussion of open questions that might lead to further insight (or perhaps kill the idea).

**Alejandra Castro**, University of Amsterdam

*The Holographic Landscape of Symmetric Product Orbifolds*

I will discuss the application of Siegel paramodular forms to constructing new examples of holography. These forms are relevant to investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. The main finding is that the landscape of symmetric product theories decomposes into two regions. In one region, the growth of the low energy states is Hagedorn, which indicates a stringy dual. In the other, the growth is much slower, and compatible with the spectrum of a supergravity theory on AdS_3. I will provide a simple diagnostic which places any symmetric product orbifold in either region. The examples I will present open a path to novel realizations of AdS_3/CFT_2.

**Lin-Qing Chen**, Okinawa Institute of Science and Technology

*Central extension and black hole entropy*

Recent developments on asymptotic symmetries and soft modes have deepened our understanding of black hole entropy and the information paradox. The asymptotic symmetry charge algebra of certain classes of spacetimes could have a nontrivial central extension, which plays a crucial role in black hole physics. The Cardy formula of the asymptotic density of states of the dual CFT has been famously used to reproduce the Bekenstein-Hawking entropy formula. However, without assuming holography, it remains obscure from the point of view of gravity how such a constant on the gravitational phase space encodes the information about the density of black hole microstates, and what the gravitational degrees of freedom accounting for the black hole entropy truly are. I will discuss my ongoing efforts of understanding these questions in the covariant phase space formalism.

**Cecilia Chirenti,** Federal University of ABC

*Probing fundamental physics with gravitational waves*

According to general relativity, the coalescence of a compact binary system creates a gravitational wave signal generically described by an inspiral-merger-ringdown waveform. The recent observations of gravitational waves by LIGO allow us to test our theory of gravity in the strong field regime. In binary black hole detections, the ringdown portion of the wave can provide tests of the no-hair theorem, the most stringent proof of the existence of astrophysical black holes and even possible hints of quantum gravity. I will present the current status of these observations and discuss future prospects.

**Marina Cortes**, University of Edinburgh

*Towards inclusion of biology in cosmology*

Cosmologists wish to explain how our universe, in all its complexity, could ever have come about. For that, we assess the number degrees of freedom in our Universe now. This plays the role of entropy in thermodynamics of the Universe, and reveals the magnitude of the problem of initial conditions to be solved. In our budget, we account for gravity, thermal motions, and finally the vacuum energy whose entropy, given by the Bekenstein bound, dominates the entropy budget today.

There is however one number which we have not accounted for: the number of degrees of freedom in our complex biosphere. What is the entropy of life? Is it sizeable enough to need to be accounted for at the Big Bang, or negligible compared to vacuum entropy?

**Astrid Eichhorn**, Heidelberg University & University of Southern Denmark

*The power of diversity - or why linking quantum gravity approaches could matter*

Linking quantum gravity approaches could be important to make progress in quantum gravity. In my talk, I will try to make this case using asymptotically safe gravity as an example. I will briefly review the status of the approach and highlight the open questions, and discuss proposed ideas how the link to other approaches could be useful to tackle these. Finally, I will emphasize the need for universality in quantum gravity, and argue that there might be universal features from quantum gravity in black-hole shadows.

**Netta Engelhardt**, Princeton University

*Central extension and black hole entropy*

**Valentina Forini**, City University of London

*AdS/CFT and string sigma-model non-perturbatively*

I will discuss progress on a non-perturbative approach to the study of string sigma-models relevant in AdS/CFT which exploits lattice field theory techniques.

**Flaminia Giacomini**, Perimeter Institute

*Quantum reference frames for space and time*

In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? In the first part of my talk, I will introduce a general method to quantise reference frame transformations within a Galilean-relativistic setting, which generalises the usual reference frame transformation to a “superposition of coordinate transformations”. We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws. In the second part of my talk, I will show how these ideas can be used to operationally define the localization of events with respect to quantum clocks, each of which identifies a “time reference frame". In particular, I will consider clocks that i) are quantum mechanical, and ii) interact, gravitationally or otherwise, with other quantum systems. We find that, when gravitational effects are important, the time localisability of events becomes a relative concept, depending on the time reference frame. We discuss the physical significance of "jumping" onto a time reference frame with respect to which specific events are localised, in the context of indefinite causal structures arising from the interplay between quantum mechanics and gravity.

**Lisa Glaser**, University of Vienna

*How much geometry is in a truncated spectral triple?*

A spectral triple consists of an algebra, a Hilbert space and a Dirac operator, and if these three fulfill certain relations to each other they contain the entire information of a compact Riemannian manifold.

Using the language of spectral triples makes it possible to generalize the concept of a manifold to include non-commutativity.

While it is possible to write down finite spectral triples, often categorized as fuzzy spaces, that describe discretized geometries, classical geometries are encoded in infinite dimensional spectral triples. However working in numerical systems (and maybe ultimately in physical systems), only a finite part of this information can be encoded, which opens the question; If we know a part of the spectrum, how clearly can we characterise a geometry.

In this talk I will present first steps towards answering this question.

**Ruth Gregory,** Durham University

*Tabletop Insights into Quantum Gravity?*

I'll describe my recent work on black hole seeded vacuum decay, and proposals for testing seeded decay in cold atom experiments. I'll conclude with speculations on seeking insight into quantum black holes via experimentally constructing quantised analog black holes.

**Renate Loll**, Radboud University of Nijmegen

*Quantum Spacetime from Lattice Gravity à la CDT*

Causal Dynamical Triangulations (CDT) is a candidate theory for quantum gravity, formulated nonperturbatively as the scaling limit of a lattice theory in terms of triangulated spacetimes. An important feature of this approach is its elegant resolution of the problem of diffeomorphism symmetry in the full, background-free quantum theory. This has enabled the concrete computation of geometric observables in a highly nonperturbative, Planckian regime, an important step in putting quantum gravity on a quantitative footing, and understanding the structure of quantum spacetime. While the need to find quantum observables describing this regime is common to all approaches, CDT provides a concrete testing ground for implementation and measurements. In particular, a new notion of quantum Ricci curvature has opened a new window on the counterintuitive properties of quantum geometry.

**Catherine Meusburger, **Friedrich-Alexander-Universität Erlangen-Nürnberg

*Ideal tetrahedra and their duals*

Ideal tetrahedra play an important role in 3d hyperbolic geometry, in the construction of hyperbolic 3-manifolds and in the computation of their volumes.

Recently they have been generalized to other 3d homogeneous spaces, namely 3d anti de Sitter space and half-pipe space, a 3d homogeneous space with a degenerate metric.

We show that generalized ideal tetrahedra correspond to dual tetrahedra in 3d Minkowski, de Sitter and anti de Sitter space. They are those geodesic tetrahedra whose faces are all lightlike.

We investigate the geometrical properties of these dual tetrahedra in a unifi ed framework. We then apply these results to obtain a volume formula for generalised ideal tetrahedra and their duals, in terms of their dihedral angles and their edge lengths.

This is joint work with Dr Carlos Scarinci, KIAS.

**Sylvie Paycha**, University of Potsdam

*How complement maps can cure divergences*

Complements offer a separating device which proves useful for renormalisation purposes. A set and its set complement are disjoint, a vector space and its orthogonal complement have trivial intersection. Inspired by J. Pommersheim and S. Garoufalidis, we define a class of complement maps which give rise to a class of binary relations that generalise the disjointness of sets and the orthogonality of vector spaces. We discuss how these reflect locality in quantum field theory and how they can be used for renormalisation purposes.

This talk is based on joint work with Pierre Clavier, Li Guo and Bin Zhang

**Nicola Pinamonti,** University of Genova

*Semiclassical Einstein equations in cosmological spacetimes*

During this talk we shall discuss the backreaction of quantum matter fields on classical backgrounds by means of the semiclassical Einstein equation.

We shall see that self consistent solutions of this coupled system exist in the case of cosmological spacetimes.

Furthermore, Einstein equations governing the backreaction will transfer quantum matter fluctuations to the metric.

**Mairi Sakellariadou**, Kings College London

*Gravitational Waves: the theorist's swiss knife*

**Lee Smolin**, Perimeter Institute

*The dynamics of difference*

A proposal is made for a fundamental theory, which is hypothesized to be a completion of both quantum mechanics and general relativity, in which the history of the universe is constituted of diverse views of itself. Views are attributes of events, and the theory’s only be-ables; they comprise information about energy and momentum transferred to an event from its causal past. A dynamics is proposed for a universe constituted of views of events, which combines the energetic causal set dynamics with a potential energy based on a measure of the distinctiveness of the views, called the variety. As in the real ensemble formulation of quantum mechanics, quantum pure states are associated to ensembles of similar events; the quantum potential of Bohm then arises from the variety.

This theory brings together results from two lines of development: energetic causal sets, developed with Marina Cortes, and the real ensemble formulation of quantum mechanics.

**Rafael Sorkin**, Perimeter Institute

*A possible causality-condition for causal sets: persistence of zero*

**Reiko Toriumi,** Okinawa Institute of Science and Technology

*The gravitational Wilson loop and the non-Abelian Stokes' theorem*

Finding suitable diffeomorphism-invariant observables to probe gravity at the Planck scale is essential in quantum gravity. The Wilson loop of the 4-dimensional Christoffel connection is a potentially interesting ingredient for the construction of such an observable. We have investigated to what extent and what form of curvature information of the underlying spacetime may be extracted from Wilson loops through a Stokes’ theorem-like relation. We present an expression for the conservation of geometric flux as the quantity related to the gravitational Wilson loop. This expression is surface-independent and it holds for a certain class of manifolds with global symmetries.

**Yasaman Yazdi,** Imperial College London

*We Don’t Live on Spatial Hypersurfaces, so Why Should Quantum Fields?*

I will discuss a number of ongoing efforts to understand quantum field properties in a manifestly spacetime framework. Entanglement entropy and causal set theory are among the topics that I will especially touch on.