Scientific Series

Quiver varieties, as introduced by Nakaijma, play a key role in representation theory. They give a very large class of symplectic singularities and, in many cases, their symplectic resolutions too. However, there seems to be no general criterion in the literature for when a quiver variety admits a symplectic resolution. In this talk, I will give necessary and sufficient conditions for a quiver variety to admit a symplectic resolution. This result builds upon work of Crawley–Boevey and of Kaledin, Lehn and Sorger. The talk is based on joint work with T. Schedler.

The methodology employed in reconstructing quantum theory involves defining a general mathematical framework that frames a landscape of possible theories and then positing principles that uniquely pick out quantum theory. In contrast, many traditional interpretations of quantum theory consider only quantum theory, not a larger space of possible theories. I will defend the modal methodology used in reconstruction by tracing the historical roots of Einstein’s distinction between principle and constructive theories. Einstein’s principle theories (exemplified by thermodynamics and special relativity) are often cited as inspiration for reconstructing quantum theory. The concept of a “physics of principles” emerged at the end of the nineteenth century in the context of the application of Lagrangian mechanics to electromagnetism. This case is an intriguing historical precedent for reconstructing quantum theory. I will also offer some reflections on how the application of a similar modal methodology in axiomatic QFT plays out. 

We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.

We argue that in quantum gravity there is no stable equilibrium state corresponding to the Born rule. Our main argument rests on the continued controversy over the physical meaning of the Wheeler-DeWitt equation. We suggest that attempts to interpret it are hampered by the conventional assumption that probabilities should be governed by a fixed Born rule. It is possible to abandon this assumption in a de Broglie-Bohm interpretation. We argue that a stable Born rule emerges only in the limiting Schrödinger regime in which the system is described by an effective (time-dependent) Schrödinger equation with an appropriate conserved current. We consider a regime in which quantum-gravitational corrections to the  Schrödinger equation induce a non-conservation of the standard current. Such a regime can be consistently described in de Broglie-Bohm theory. As a result, quantum-gravitational effects can generate non-equilibrium deviations from the Born rule even starting from an initial equilibrium state. We provide estimates for such effects in an inflationary de Sitter background.

The recent detection of the binary neutron star merger GW170817 by LIGO and Virgo was followed by a firework of electromagnetic counterparts across the entire electromagnetic spectrum. In particular, the ultraviolet, optical, and near-infrared emission is consistent with a kilonova that provided strong evidence for the formation of heavy elements in the merger ejecta by the rapid neutron capture process (r-process). In this talk, I will discuss the state of the art in modeling neutron star mergers from first principles, which represents a multi-physics challenge involving all four fundamental forces and petascale computing. I will present recent results from general-relativistic magnetohydrodynamic simulations and discuss possible scenarios and mass ejection mechanisms that can give rise to the observed kilonova features. In particular, I will argue that massive winds from neutrino-cooled post-merger accretion disks most likely synthesized the heavy r-process elements in GW170817. I will show how this finding (at least partially) concludes the quest for the cosmic origin of the heavy elements, which has been an enduring mystery for more than 70 years.

Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. In the most well-studied example, the pilot-wave theory of de Broglie and Bohm, it is well established that the Born rule may be understood to arise from a process of dynamical relaxation. This 'quantum relaxation' may have taken place in the very early universe and could have left imprints on the cosmic microwave background (CMB). Such imprints amount to signatures of the decay of early violations of the Born rule. In this colloquium we summarise recent progress in making detailed predictions and in comparing them with the reported large-scale anomalies in the CMB data.

Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. A natural question to ask is whether the theory is stable under small perturbations away from equilibrium. We compare and contrast two examples: de Broglie's 1927 pilot-wave theory and Bohm's 1952 reformulation thereof. It is well established that in de Broglie's dynamics initial deviations from equilibrium will relax. We show that this is not the case for Bohm's dynamics: initial deviations from equilibrium do not relax and in fact grow with time. On this basis we argue that Bohm's dynamics is untenable as a physical theory (while de Broglie's dynamics remains a viable candidate). We advocate stability as a general selection criterion for hidden-variables theories.

All physical constraints of the conformal bootstrap in principle arise by applying linear functionals to the conformal bootstrap equation. An important goal of the bootstrap program is to identify a suitable basis for the space of functionals -- one that would allow us to solve crossing analytically. In my talk, I will describe two particularly convenient choices of the basis for the 1D conformal bootstrap. The two bases manifest the crossing symmetry of the four-point function of a generalized free boson and generalized free fermion respectively. I will use the bases to study small deformations of the two theories. Assuming no new operators appear in the OPE, the generalized free fermion allows no small deformation, and the generalized free boson allows a one-parameter deformation, which coincides with the AdS_2 four-point contact interaction at the leading order. Time allowing, I will discuss the connection of this work to the conformal bootstrap a la Polyakov.

Large scale structure surveys are one of our primary tools for answering open questions in cosmology like: What is the physics behind dark energy? Is gravity well described by general relativity on cosmological scales, or does that description need to be extended? In order to take full advantage of the information contained in survey data, however, we must ensure that we understand our data’s sensitivity to new physics and that our analyses are not biased by systematics. In my talk I’ll describe work I have been doing in this aim for the Dark Energy Survey (DES). I’ll begin with an introduction to how we can use data from surveys like the DES to test LCDM, including approaches to constraining extensions to general relativity with cosmological data. I’ll use that discussion to motivate a so-called growth-geometry split analysis, a consistency test of LCDM that works by comparing constraints from probes of structure growth and expansion history, and will discuss the status of such an analysis applied to DES data. I’ll also give an overview of the blinding strategy planned for future multi-probe DES cosmology analyses.

I'll discuss an ongoing project of mine with Dinakar Muthiah and Oded Yacobi, which is based on ideas of Kreiman-Lakshmibai-Magyar-Weyman.  It is aimed at developing a "nice" standard monomial theory for the affine Grassmannian in type A, where "nice" means hopefully close in spirit to Hodge's classical standard monomial theory for finite dimensional Grassmannians.

We consider planar hairy black holes in five dimensions with a real scalar field in the Breitenlohner-Freedman window and show that is possible to derive a universal formula for the holographic speed of sound for any mixed boundary conditions of the scalar field. As an example, we locally construct the most general class of planar black holes coupled to a single scalar field in the consistent truncation of type IIB supergravity that preserves the SO(3)xSO(3) R-symmetry group of the gauge theory. We obtain the speed of sound for different values of the vacuum expectation value of a single trace operator when a double trace deformation is induced in the dual gauge theory. In this particular family of solutions, we find that the speed of sound exceeds the conformal value. Finally, we generalize the formula of the speed of sound to arbitrary dimensional scalar-metric theories whose parameters lie within the Breitenlohner-Freedman window

In this talk I show how to systematically classify all possible alternatives to the measurement postulates of quantum theory. All alternative measurement postulates are in correspondence with a representation of the unitary group. I will discuss composite systems in these alternative theories and show that they violate two operational properties: purification and local tomography. This shows that one can derive the measurement postulates of quantum theory from either of these properties. I will discuss the relevance of this result to the field of general probabilistic theories. In a second part of the talk I will discuss work in progress and directions for future research. I will show how to generalise the framework used to theories which have different pure states and dynamics than quantum theory. I will discuss two types of theories which can be studied in this framework: Grassmannian theories (same dynamical group and different pure states to quantum theory) and non-linear modifications to the Schrodinger equation (same pure states and different dynamical group).