Scientific Series

I will explain a recent joint work with A. Shapiro in which we prove that the quantized K-theoretic BFN Coulomb branch ring associated to a quiver gauge theory is isomorphic to a quantum upper cluster algebra, when the gauge theory quiver is without 1-cycles. The new ingredient needed to upgrade our earlier partial results in this direction is a precise description of the image of the Coulomb ring for gauge group G inside the localized equivariant K-theory of the affine Grassmannian Gr_T, where T \subset G is the maximal torus. This description combines conditions on residues at possible simple poles at shifted root hyperplanes with divisibility conditions controlled by the representation N determining the matter content of the theory.

We study subregion algebras in classical and perturbative quantum gravity on half-spaces of event horizons. We construct half-sided supertranslation generators by extending subregion phase spaces of the event horizon to include doubled pairs of edge modes obtained from splitting the horizon. These edge modes carry a corner symplectic form that gives rise to canonical generators of half-sided boosts and translations, the former of which is the area operator at the corner while the latter corresponds to null time evolution along the horizon. The charges act nontrivially on gravitationally dressed bulk observables, such that subalgebras take the form of a crossed product by the associated automorphism group. Quantizing the extended phase space after linearizing around a black hole, we obtain for each cut a Type II$_{\infty}$ von Neumann algebra whose entropy coincides with the generalized entropy of that cut. The nesting property of the resulting one-parameter family of subalgebras implies a generalized second law for linearized perturbations of Killing horizons. Finally, we use gravitational half-sided modular inclusion algebras to prove quantum focusing along Killing horizons in the perturbative quantum gravity regime.

I will revisit the canonical quantization of General Relativity in the self-dual formulation in the presence of a cosmological constant, discussing the normalizability of graviton states over the de Sitter spacetime. Time permitting, I will explain how the physics of the Hamiltonian constraint is analogous to the quantum Hall effect, with the cosmological constant playing the role of a quantum gravitational Hall resistivity.

Physics has been driven by the discovery of novel phases of matter, largely in materials.  Recently, the advent of both quantum error correction and machine learning, viewed as physical phenomena, has compelled us to revisit the notion of a phase itself.  I will show how decodable/undecodable regimes of codes constitute distinct phases in a precise sense, and they furnish machine unlearnable/learnable phases of data.  I will demonstrate how conditional mutual information (CMI) serves as an essential quantity in characterizing the corresponding phases and transitions and thus provides a new diagnostic for both error correction thresholds and machine learnability of quantum and classical systems, including real-world data.  

In this broad-audience talk, I will discuss the basics of gravitational wave theory and the major achievements in the field following the direct observation of the first gravitational wave signal in 2015. Then, I will discuss how gravitational wave data are used to test the validity of general relativity and motivate my current research on the subject.

Although there are good reasons to believe that quantum states are sometimes relativized to observers, there are difficulties for the view that quantum states can only be relativized to conscious macroscopic observers, and also for the view that quantum states can be relativized to any physical system. In this talk, I will argue for an alternative `emergence' approach such that we can indeed write down a description relative to any physical system, but the full formalism of quantum theory emerges only in the limit as the reference system becomes large. If this is true, it poses a challenge for attempts to understand the emergence of the classical regime from the quantum world, since our standard quantum descriptions may presuppose a classical system to which they are relativized. I will describe how this idea might give new insight into Extended Wigner's Friend paradoxes and the measurement problem, and then sketch some ideas for how we might generalize beyond quantum mechanics to characterize descriptions relative to other kinds of reference systems.

Given a vertex operator algebra V, one can define sheaves of conformal blocks on moduli spaces of curves following constructions of Ben-Zvi--Frenkel and Damiolini--Gibney--Tarasca. When V is strongly rational, these sheaves are vector bundles equipped with a projectively flat connection. In this talk, I will explain how these bundles satisfy the compatibility conditions required to form a modular functor. A key consequence of this result is that the category C_V of admissible V-modules is a modular fusion category. This provides a purely algebro-geometric construction of the tensor product on C_V, which is expected to agree with the tensor product defined by Huang and Lepowsky using analytic methods. Time permitting, I will discuss open questions concerning extensions beyond the rational setting. This is joint work with Lukas Woike.

Small naked singularities—those not shielded by a macroscopic event horizon—are ubiquitous in classical General Relativity. Their existence constitutes apparent violations of the weak cosmic censorship conjecture, which asserts that physically reasonable solutions should appear regular to asymptotic observers. In this talk, we will show how the inclusion of stringy and quantum effects resolves these pathologies by uplifting naked singularities into fully regular configurations. Focusing on critical gravitational collapse as a concrete example, we demonstrate that a proper quantum treatment replaces naked singularity formation with black hole formation. This suggests that cosmic censorship is not fundamentally a property of classical General Relativity, but rather emerges only once quantum gravitational effects are taken into account.

Since the 1980s, simulation of quantum many-body systems has been a leading candidate for practical quantum advantage. Yet computing thermal equilibrium properties, a central pillar of this vision, still lacks an end-to-end algorithmic solution. Today, I will present a general-purpose algorithmic and analytic framework for preparing quantum thermal states as a quantum analog of Markov chain Monte Carlo (MCMC) methods, and as a workable model of nature’s system-bath interaction.