Scientific Series

In classical General Relativity (GR), an observer falling into an astrophysical black hole (BH) is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. I outline theoretical and phenomenological arguments for these departures. I will then discuss the tentative observational evidence for Planck-scale structure near BH horizons, seen as "echoes" in LIGO gravitational wave observations,  which has now been found by three independent groups. Finally, I present preliminary analysis which strongly suggest formation of a highly spinning black hole within 0.5 second of GW170817 binary neutron star merger, based on prominent echoes in the LIGO strain data. 

Let be a complex semisimple algebraic group of adjoint type and the wonderful compacti
cation. We show that the closure in \overline{G} of the centralizer of a regular nilpotent is isomorphic to the Peterson variety. We generalize this result to show that for any regular , the closure of the centralizer in is isomorphic to the closure of a general -orbit in the flag variety. We consider the family of all such centralizer closures, which is a partial compactication of the universal centralizer. We show that it has a natural log-symplectic Poisson structure that extends the usual symplectic structure on the universal centralizer.

In this talk, I'd like to explain how quantum integrability and (q-deformed) W-algebraic structure arise from the moduli space of quiver gauge theory. It'll be also shown that our construction gives rise to a new family of W-algebras. 

We are fortunate to live in an era of great discoveries in particle physics and cosmology, and most of the theoretical understanding that made this possibile is based on effective field theories. In this talk, I will show how these powerful techniques can be applied across the spectrum of theoretical physics, and allow us to draw unexpected connections among very different systems. To illustrate this, I will discuss two interesting but very different phenomena, and show how they can both be described using a point-like particle effective theory. The first phenomenon I will consider is superradiance---a dissipative phenomenon by which a spinning object can amplify the intensity of scattered radiation, or be unstable by creation of particles in a bound state. This phenomenon is particularly interesting when applied to spinning black holes, and in this context it has recently received significant attention as a possible probe of ultra-light particle beyond the Standard Model. The second phenomenon I will discuss is the existence of roton excitations in superfluid He4. By treating rotons as point-like particles--albeit of a very special kind--I will write down an effective theory that describes the motion of rotons in the medium at equilibrium as well as their couplings to sound waves and generic fluid flows. This approach allows us to correct classic results by Landau and Khalatnikov on roton-phonon scattering, and to pose and answer the intriguing question: do rotons sink or float? 

Two seemingly different quantum field theories may secretly describe the same underlying physics — a phenomenon known as “duality”. Duality has been proved powerful in condensed matter physics, since many difficult questions can be drastically simplified in certain “dual” pictures. This is especially valuable for strongly interacting many-body problems, for which traditional tools (such as perturbation theory) are often not applicable. 

Recent developments on dualities have also revealed deep connections between several previously unrelated topics in modern condensed matter physics, including topological insulators, fractional quantum Hall effects and quantum phase transitions. Connections were also made between dualities in condensed matter physics and in high energy physics. I will give a brief review of some of these developments.

The study of black holes has revealed a deep connection between quantum information and spacetime geometry. Its origin must lie in a quantum theory of gravity, so it offers a valuable hint in our search for a unified theory. Precise formulations of this relation recently led to new insights in Quantum Field Theory, some of which have been rigorously proven. An important example is our discovery of the first universal lower bound on the local energy density. The energy near a point can be negative, but it is bounded below by a quantity related to the information flowing past the point.

I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order EΔt/ℏ, where E the average energy of the signal, and Δt is the amount of time for which detectors operate. The bound does not depend on the size or mass of the emitting and receiving systems, nor on the nature of the signal. No restrictions on preparing and processing the signal are imposed. 
As an example, I consider the encoding of information in the transverse or angular position of a signal emitted and received by systems of arbitrarily large cross-section. In the limit of a large message space, quantum effects become important even if individual signals are classical, and the bound is upheld.

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.