Talks

Tensor network/spacetime correspondences explore the exciting idea that geometric information about a quantum state might be related to the actual geometry that the state describes in a quantum gravitational setting. I will give an overview of a new type of correspondence between global de Sitter spacetime and the MERA. This simple correspondence is already enough to see several features of de Sitter gravity emerge, such as cosmic no-hair and horizon complementarity. I will also comment on some more speculative topics like complexity = action and possible future directions.

The Hecke category is a certain monoidal category of constructible sheaves on a flag variety that categorifies the Hecke algebra and plays an important role in geometric representation theory. In this talk, I will discuss a monoidal Koszul duality relating the Hecke category of Langlands-dual (Kac–Moody) flag varieties, categorifying a certain involution of the Hecke algebra. In particular, I will try to explain why one needs to introduce a monoidal category of "free-monodromic tilting sheaves" to formulate this duality. (Joint with P.N. Achar, S. Riche, and G. Williamson.)

Compatibility of asymptotic safety with UV-completions of matter theories may constrain the underlying microscopic dynamics of quantum gravity. Within truncated RG-flows, a weak-gravity bound originates from the loss of quantum scale-invariance in the matter system. Further constraints could arise when linking Planck-scale to electroweak-scale dynamics. Within the constrained region, gravitationally induced scale-invariance could UV-complete the Standard Model, and moreover explain free parameters such as fermion masses and gauge couplings.

I will describe the recently developed bimetric theory of fractional quantum Hall states. It is an effective theory that includes the Chern-Simons term that describes the topological properties of the fractional quantum Hall state, and a non-linear, a la bimetric massive gravity action that describes gapped Girvin-MacDonald-Platzman mode at long wavelengths. The theory reproduces the universal features of the chiral lowest Landau level (LLL) FQH states that lie beyond the reach of pure Chern-Simons theory, such as the projected static structure factor and the Girvin-MacDonald-Platzman algebra. The action of particle-hole transformation on the theory is particularly transparent. Familiar quantum Hall observables acquire a geometric interpretation in the bimetric language

Quantum error correction -- originally invented for quantum computing -- has proven itself useful in a variety of non-computational physical systems, as the ideas of QEC are broadly applicable. In this talk, I'll mention a few examples of error correction in the wild, including the recent discovery that the AdS/CFT correspondence implements quantum error correction.  We will then study the hypothesis that any local bulk operator in AdS can be reconstructed using only a causally disconnected subregion of the CFT.  This hypothesis has been proven under the assumption that error correction in AdS/CFT is exact, but this assumption is not expected to be true.  Fortunately, recent advances in the theory of approximate quantum error correction have emerged.  We will review these results on recoverability and approximate quantum error correction, as well as AdS/CFT and the so-called entanglement wedge reconstruction hypothesis.  We will then prove the entanglement wedge hypothesis robustly and find an explicit formula for reconstructed bulk operators.  If time permits, we will explore a generalization of the theory of universal recovery channels to the case of finite-dimensional von Neumann algebras.

Our sense of smell is extraordinarily good at molecular recognition: we can identify tens of thousands of odorants unerringly over a wide concentration range. The mechanism by which this happens is still hotly debated. One view is that molecular shape governs smell, but this notion has turned out to have very little predictive power. Some years ago I revived a discredited theory that posits instead that the nose is a vibrational spectroscope, and proposed a possible underlying mechanism, inelastic electron tunneling. In my talk I will review the history and salient facts of this problem and describe some recent experiments, both on fruit flies and on humans, that go some way towards answering the question. 

BCS bogoliubon excitations, quantum Hall effect (QHE) and Landau levels (QHE handout)