Scientific Series

We'll explain the slogan of the title: a cluster variety is a space associated to a quiver, and which is built out of algebraic tori.

They appear in a variety of contexts in geometry, representation theory, and physics. We reinterpret the definition as: from a quiver (and some additional choices) one builds an exact symplectic 4-manifold from which the cluster variety is recovered as a component in its moduli space of Lagrangian branes. In particular, structures from cluster algebra govern the classification of exact Lagrangian surfaces in Weinstein 4-manifolds.

This is joint work with Vivek Shende and David Treumann.

100 years after the existence of gravitational waves was first postulated by Albert Einstein, the LIGO and Virgo Collaborations detected gravitational waves for the first time on September 14, 2015. The gravitational waves originated from a pair of black holes that merged over one billion years ago.  The merger was so powerful that it shook the very fabric of space and sent a ripple across the Universe that we observed here on Earth at present day. Although this event was but a blip in a sea of data taken by various experiments over the last several decades, it represents a paradigm shift in how we study our Universe.

In this colloquium, I will present some of the history of this great discovery and what it means for our future at the dawn of gravitational wave astronomy.

In quantum theory every state can be diagonalised, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This fact is crucial in quantum statistical mechanics, as it provides the foundation for the notions of majorisation and entropy. A natural question then arises: can we give an operational characterisation of them? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalised: Causality, Purity Preservation, Purification, and Pure Sharpness. If we add the Permutability and Strong Symmetry axioms, which are in fact completely equivalent in theories satisfying the other axioms, the diagonalisation result allows us to define a well-behaved majorisation preorder on states. Indeed this majorisation criterion fully captures the convertibility of states in the operational resource theory of purity where random reversible transformations are regarded as free operations. One can also put forward two alternative notions of purity as a resource: one where free operations are unital channels, and another where free operations are generated by reversible interactions with an environment in the invariant state. Under the validity of the above axioms, all these definitions are in fact equivalent, i.e. they all lead to the same preorder on states, which is given by majorisation, in the very same way as in quantum theory.

Dark matter can be a thermal relic exponentially lighter than
the weak scale without being exponentially weakly coupled. I will present
three mechanisms to obtain light thermal dark matter with sizable
self-interactions and couplings to the Standard Model.

We are currently in an era of precision cosmology, but is it an era of accurate cosmology? By measuring cosmological parameters with many independent probes we can convince ourselves that our measurements of the parameters are indeed correct. Thanks to recent progress, strong gravitational lensing is now a powerful probe of cosmology. In this talk I'll report on a measurement of H0 at 5% precision using two strongly lensed quasars and a 20% measurement on the equation of state of dark energy using a double source plane lens. I'll also present new results from a z=1 strong lensing cluster where the dark matter profile deviates significantly from the NFW profile that is predicted by cold dark matter simulations, but it is consistent with simulations of self-interacting dark matter. I'll finish by discussing how upcoming wide area surveys can provide hundreds of exotic strong lenses that can be used for precise and accurate cosmology over the next decade.

Recent findings on quantitative growth patterns have revealed striking generalities across the tree of life, and recurring over distinct levels of organization. Growth-mass relationships in 1) individual growth to maturity, 2) population reproduction, 3) insect colony enlargement and 4)  community production across wholeecosystems of very different types, often follow highly robust near ¾ scaling laws. These patterns represent some of the most general relations in biology, but the reasons they are so strangely similar across levels of organization remains a mystery. The dynamics of these distinct levels are connected, yet their scaling can be shown to arise independently, and free of system-specific properties. Numerous experiments in prebiotic chemistry have shown that minimal self-replicating systems that undergo template-directed synthesis, typically show reaction orders (ie. growth-mass exponents) between ½ and 1. I will outline how modifications to these simplified reaction schemes can yield growth-mass exponents near ¾, which may offer insight into dynamical connections across hierarchical systems.

General relativity is invariant under diffeomorphisms, and

excitations of the metric corresponding to diffeomorphisms

are nonphysical.  In the presence of a boundary, though --

including a boundary at infinity -- the Einstein-Hilbert

action with suitable boundary terms is no longer fully

invariant, and certain diffeomorphisms are promoted to

physical degrees of freedom.  After briefly describing how

this happens in (2+1)-dimensional AdS gravity, I will

report on work in progress on the asymptotically flat case,

for which the newly dynamical diffeomorphisms are the

superrotations, and the boundary action is related to

coadjoint orbits of the Virasoro group and Hill's equation.

Current observations provide precise but limited information about inflation and reheating. Theoretical considerations, however, suggest that the early universe might be filled with a large number of interacting fields with unknown interactions.  How can we quantitatively understand the dynamics of perturbations during inflation and reheating in such scenarios and when only limited

constraints are available from observations?   Based on a precise

mapping between particle production in cosmology to resistivity in disordered, quasi one-dimensional wires, I will provide a statistical framework to resolve such seemingly intractable calculations. A number of phenomenon in disordered wires find an analogue in particle production. For example, Anderson localization in quasi one-dimensional wires can be directly mapped to exponential particle production in the early universe. The talk will be focussed on the general framework and some toy examples, though in the end I will discuss possible (future) applications to calculating observables.

Spectral distortions of the CMB provide a powerful new probe of early Universe processes. Even if so far no average spectral distortion has been seen, LCDM does predict several signals that are within reach of current technology. In this talk, I will give a broad brush overview of our most recent understanding of the formation and evolution of distortions in the early Universe, highlighting guaranteed LCDM signals and what we hope to learn from them about the Universe we live in.

We present results from a study of Euclidean dynamical triangulations in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior, and that once this tuning is performed, our simulations provide evidence in support of the asymptotic safety scenario for gravity.  We discuss our motivation for the tuning and present our numerical results. Finally, we discuss what our simulations imply for the dimension of the ultraviolet critical surface, which sets the number of free parameters in the theory.

Recent developments in our understanding of black hole evaporation and the information paradox suggest that effects from quantum gravity are not necessarily hidden at the Planck scale. They might even one day be testable by gravitational wave measurements. To prepare ourselves, we must first understand what quantum gravity really means. Thankfully, we are pre-armed with a deep principle about gravity—that spacetime is really a hologram—and a powerful model for making this idea precise: gauge/gravity duality. The present challenge is to translate our questions about gravity into the natural language of the dual conformal field theory (CFT). I will describe the foundation for such a program that links the integral geometry of a gravitational spacetime to a CFT operator product expansion.

As discussed in last week’s colloquium, the use of the p-adic metric in state space provides a route to resolving the Bell Theorem in favour of realism and local causality, without fine tuning. Here the p-adic integers provide a natural way to describe the fractal geometry of Invariant Set Theory’s state space. In this talk I first explore the role of complex numbers in Invariant Set Theory (arXiv:1605.01051), and describe a novel realistic perspective on quantum interferometry. Then I will describe a programme of work to synthesise quantum and gravitational physics realistically and causally within the framework of Invariant Set Theory. I will describe a p-adic generalisation of the field equations of General Relativity, and discuss the consequent novel perspectives for understanding the dark (energy and matter) universe.