Talks

The Ryu-Takayanagi (RT) formula was originally introduced to compute the entropy of holographic boundary conformal field theories. In this talk, I will show how this formula can also be understood as the entropy of an algebra of bulk gravitational observables. Specifically, I will demonstrate that any Euclidean gravitational path integral, when it satisfies a simple set of properties, defines Hilbert spaces associated with closed codimension-2 asymptotic boundaries, along with type I von Neumann algebras of bulk observables acting on these spaces. I will further explain how the path integral naturally defines entropies on these algebras, and how an interesting quantization property leads to a standard state-counting interpretation. Finally, I will show that in the appropriate semiclassical limits, these entropies are computed via the RT formula, thereby providing a bulk Hilbert space interpretation of the RT entropy.

Maturing Pulsar Timing Arrays are expected to inaugurate the era of nano-hertz GW astronomy in the coming days under the auspices of the International Pulsar Timing Array. Implications of ongoing IPTA efforts for astrophysics and cosmology will be discussed while focussing on PTA contributions. Ongoing IPTA efforts should lead to persistent multi-messenger GW astronomy with massive BH binaries especially during the Square Kilometre Array era, and its implications will be discussed.

The Moore-Tachikawa conjecture posits the existence of certain 2-dimensional topological quantum field theories (TQFTs) valued in a category of complex Hamiltonian varieties. Previous work by Ginzburg-Kazhdan and Braverman-Nakajima-Finkelberg has made significant progress toward proving this conjecture. In this talk, I will introduce a new approach to constructing these TQFTs using the framework of shifted symplectic geometry. This higher version of symplectic geometry, initially developed in derived algebraic geometry, also admits a concrete differential-geometric interpretation via Lie groupoids and differential forms, which plays a central role in our results. It provides an algebraic explanation for the existence of these TQFTs, showing that their structure comes naturally from three ingredients: Morita equivalence, as well as multiplication and identity bisections in abelian symplectic groupoids. It also allows us to generalize the Moore-Tachikawa TQFTs in various directions, raising interesting questions in Lie theory and Poisson geometry. This is joint work with Peter Crooks.

Condensation of topological defects is the foundation of the modern theory of bulk-boundary correspondence, also known as topological holography. In this talk, I discuss string condensation in 3+1D topological orders, which plays a role analogous to anyon condensation in 2+1D topological orders. I will demonstrate through examples how they correspond to 2+1D symmetry enrichd phases, including both gapped and gapless phases. Then I give a detailed analysis of string condensaiton in 3+1D discrete gauge theories. I compute the outcome of the condensation, namely the category of excitations surviving the condensation. The results suggest that a complete topological holography for 2+1D phases can only be established by taking into account all possible ways of condensing strings in the bulk 3+1D topological order.

The matter power spectrum on subgalactic scales is very weakly constrained so far. While inflation predicts a nearly scale-invariant primordial power spectrum down to very small scales, many new physics scenarios can lead to significantly different predictions, such as axion dark matter in the post-inflationary scenario, vector dark matter produced during inflation, early matter domination, kinetic misalignment axions, self-interacting dark matter, atomic dark matter, etc. Therefore, any successful measurement on the matter power spectrum tests inflation extensively and probes early universe dynamics and the nature of dark matter, making it a new frontier in cosmology and dark matter physics. We proposed observing fast radio bursts (FRB) with solar-system scale interferometry by sending radio telescopes to space, which allows us to greatly expand the sensitivity on the matter power spectrum from Mpc to AU scales. Two sightlines looking at the same FRB source can sample different regions of the Universe in the transverse direction and thus obtain an arrival time difference that depends on the matter power spectrum. Our calculations show that this setup will be sensitive to the scale-invariant power spectrum predicted by inflation on small scales and can also probe QCD axion miniclusters predicted in the post-inflationary scenario.