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Corner symmetries are those diffeomorphisms that become physical in codimension two, in that they support non-zero Noether charges. Recently we have shown how to extend phase space so that all such charges are integrable and give a representation of the corner symmetry algebra on this extended phase space. More recently we have studied the coadjoint orbits of what we now call the universal corner symmetry. One finds that certain complementary subalgebras, the extended corner symmetry and the asymptotic corner symmetry, can be associated with finite-distance and asymptotic corners, respectively. There is a simple geometric interpretation here in terms of an Atiyah Lie algebroid over a corner, whose structure group is the universal corner symmetry. The local geometry of a classical spacetime is encoded in related geometric structures.

This talk reviews the use of radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus. The partition function is given by a particular transition amplitude between two states which are defined on the Riemann surfaces that define the (singular) foliation of the handlebody. By requiring that the only singularities of the gauge field inside the handlebody must be compatible with Wilson loop insertions, we find that the Wilson loop shifts the holonomy of the initial state. Together with an appropriate choice of normalization, this procedure selects a unique state in the Hilbert space obtained from a Kähler quantization of the theory on the constant-radius Riemann surfaces. Radial quantization allows us to find the partition functions of Abelian Chern-Simons theories for handlebodies of arbitrary genus. For non-Abelian compact gauge groups, we show that our method reproduces the known partition function and Wilson loop VEVs at genus one.

I will present an analysis of the Hamiltonian formulation of gauge theories on manifolds with corners in the particular, yet common, case in which they admit an equivariant momentum map. In the presence of corners, the momentum map splits into a part encoding “Cauchy data” or constraints, and a part encoding the “flux” across the corner. This decomposition plays an important role in the construction of the reduced phase space, which then becomes an application of symplectic reduction in stages for local group actions. The output of this analysis are natural "corner" Poisson structures, leading to the concept of (classical) flux superselection sectors as their symplectic leaves. This is based on a collaboration with A. Riello. My talk will cover the general framework of corner superselection, while Riello’s talk will deal with its application to null boundaries and soft charges.

Based on arXiv:2208.04334. We consider oscillons - localized, quasiperiodic, and extremely long-living classical solutions in models with real scalar fields. We develop their effective description in the limit of large size at finite field strength. Namely, we note that nonlinear long-range field configurations can be described by an effective complex field ψ(t, x) which is related to the original fields by a canonical transformation. The action for ψ has the form of a systematic gradient expansion. At every order of the expansion, such an effective theory has a global U(1) symmetry and hence a family of stationary nontopological solitons - oscillons. The decay of the latter objects is a nonperturbative process from the viewpoint of the effective theory. Our approach gives an intuitive understanding of oscillons in full nonlinearity and explains their longevity. Importantly, it also provides reliable selection criteria for models with long-lived oscillons. This technique is more precise in the nonrelativistic limit, in the notable cases of nonlinear, extremely long-lived, and large objects, and also in lower spatial dimensions. We test the effective theory by performing explicit numerical simulations of a (d+1)-dimensional scalar field with a plateau potential. 

Zoom link: https://pitp.zoom.us/j/98801138609?pwd=VUJsZm41bnpBQzFoUEFwcUV6SG5Xdz09

I will discuss the small speed of light expansion of general relativity, utilizing the modern perspective on non-Lorentzian geometry. The leading order in the expansion leads to an action that corresponds to the electric Carroll limit of general relativity, of which I will highlight some interesting properties. The next-to-leading order will also be obtained, which exhibits a particular subsector that correspond to the magnetic Carroll limit, which features a solution that describes the Carroll limit of a Schwarzschild black hole. The incorporation of a cosmological constant in the Carroll (or ultra-local) expansion will also be commented on. Finally, I will describe how Carroll symmetry and geometry arises on the world-sheet of certain limits of string theory sigma models.

Z2 lattice gauge theories (LGTs) coupled to dynamical matter show rich physics, including topological phases with anyons (toric code) and fractionalized Fermi liquids, with potential realizations in strongly correlated quantum matter. In this talk I report on recent progress — theoretical and experimental — in performing analog quantum simulations of such models. Starting from several distinct zero-dimensional building blocks I will move on to discuss extensions to extended 1D and 2D systems, including the realization of the plaquette operators in 2D. Next I will discuss how experimental imperfects, such as gauge-symmetry breaking errors, impact quantum simulations, and how they can be overcome. Then I will show how the insights gained lead us to an inherently stable protocol for quantum simulations of Z2 LGTs with dynamical matter with existing Rydberg tweezer arrays. I will close with an outlook and by discussing possible near-term experimental goals ranging from disorder-free localization to finite-temperature deconfinement transitions.

Zoom link:  https://pitp.zoom.us/j/91839919649?pwd=Tm1uOVljWUV3R05aUkxFVkFzN3lIZz09

In this talk I will share our recent work in developing statistical models based on machine learning methods. In particular, I will discuss posterior sampling in low- and high-dimensional spaces and connect this to two ongoing projects: measuring the small-scale distribution of dark matter and estimating the expansion rate of the Universe. I will discuss how the speed and the accuracy gained by these models are essential for the large volumes of data from the next generation sky surveys. I will finish by mentioning a few other projects and a new initiative for interdisciplinary collaboration in astrophysics and data sciences. 

Zoom link:  https://pitp.zoom.us/j/98316228305?pwd=UWwrZkIwUG1QZFBkYzc1eVdNSW1Ldz09

The flat space holography program aims at describing quantum gravity in asymptotically flat spacetime in terms of a dual lower-dimensional field theory. Two different roads to construct flat space holography have emerged. The first consists of a 4d bulk / 3d boundary duality, called Carrollian holography, where 4d gravity is suggested to be dual to a 3d Carrollian CFT living on the null boundary of the spacetime. The second is a 4d bulk / 2d boundary duality, called celestial holography, where 4d gravity is dual to a 2d CFT living on the celestial sphere. I will argue that these two seemingly contradictory proposals are actually related. The Carrollian operators will be mapped to the celestial operators using an appropriate integral transform. The Ward identities of the sourced Carrollian CFT, encoding the gravitational flux-balance laws, will be shown to reproduce those of the 2d celestial CFT, encoding the bulk soft theorems.

The goal of this talk is to discuss residual gauge symmetries in electromagnetism and gravity in Dirac's front form. Working in the light-cone gauge, I will demonstrate how the large gauge transformations and BMS supertranslations may be obtained from residual gauge invariance of the Hamiltonian action. The residual gauge symmetries in this (2+2) formulation share some striking similarities with the asymptotic symmetries in the conventional (3+1) Hamiltonian formulation. I will illustrate this fact using the example of electromagnetism and show how the the zero modes play a crucial role akin to boundary degrees of freedom in the asymptotic analysis at spatial infinity à la Henneaux-Troessaert.

In this introductory talk, I will present a new perspective about quantum gravity which is rooted deeply in a renewed understanding of local symmetries in Gravity that appears when we decompose gravitational systems into subsystems. I will emphasize the central role of the corner symmetry group in capturing all the necessary data needed to glue back seamlessly quantum spacetime regions. I will present how the charge conservation associated with these symmetries encoded the dynamics of null surfaces. Finally, I will also present how the representation theory of the corner symmetry arises and provides a representation of quantum geometry, and I will show that deformations of this symmetry can be the explanation for a fundamental planckian cut-off. I will also mention how these symmetry groups reduce to asymptotic symmetry groups and control asymptotic gravitational dynamics when the entangling sphere is moved to infinity. If time permits, I will explain how these symmetries control asymptotic gravitational dynamics. And I will describe how they provide a new picture of the nature of quantum radiation. Overall, this new paradigm allows to connect semi-classical gravitational physics, S-matrix theory, and non-perturbative quantum gravity techniques. The talk's goal is to give an overall flavor of how these connections appear from an elementary understanding of symmetries.