Talks

In this talk I revisit the canonical framework for general relativity in its connection-frame field formulation, exploiting its local holographic nature. I will show how we can understand  the  Gauss law, the Bianchi identity and the space diffeomorphism constraints as conservation laws for local surface charges. These charges being respectively the electric flux, the dual magnetic flux  and momentum charges. Quantization of the surface charge algebra can be done in terms of Kac-Moody edge modes. This leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. Taking a finite dimensional truncation of this quantization yields states of quantum geometry,  dubbed `Poincaré charge networks’, which carry a representation of the 3D diffeomorphism boundary charges on top of the SU(2) fluxes and gauge transformations. This opens the possibility to have for the first time a framework where spatial diffeomorphism are represented at the quantum level. Moreover, our construction leads naturally to the picture that the relevant geometrical degrees of freedom live on boundaries, that their dynamics and the fabric of quantum space itself is encoded into their entanglement, and it is designed to offer a new setting to study the coarse-graining of gravity both at the classical and the quantum levels.

As of late March 2020, Covid-19 has already secured its status among the most expansive pandemics of the last century. Covid-19 is caused by a coronavirus--SARS-CoV-2--that causes a severe respiratory disease in a fraction of those infected, and is typified by several important features: ability to infect cells of various kinds, contagiousness prior to the onset of symptoms, and a widely varying experience with disease across patient demographics.

In this seminar, I discuss the many lessons that the scientific community has learned from Covid-19, including insight from molecular evolution, cell biology, and epidemiology. I discuss the role of mathematical and computational modeling efforts in understanding the trajectory of the epidemic, and highlight modern findings and potential research questions at the interface of virology and materials science. I will also introduce areas of inquiry that might be of interest to the physics community.

Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. In particular their fundamental degrees of freedom are not point-like. This leads to a non-trivial cutting (C) and sewing (S) problem: 
(C) Which gauge invariant degrees of freedom are associated to a region with boundaries? 
(S) Do the gauge invariant degrees of freedom in two complementary regions R and R’ unambiguously comprise *all* the gauge-invariant degrees of freedom in M = R ∪ R’ ? Or, do new “boundary degrees of freedom” need to be introduced at the interface S = R ∩ R’ ?
In this talk, I will address and answer these questions in the context of Yang-Mills theory. The analysis is carried out at the level of the symplectic structure of the theory, i.e. for linear perturbations over arbitrary backgrounds. I will also discuss how the ensuing results translate into a quasilocal derivation of the superselection of the electric flux through the boundary of a region, and into a novel gluing formula which constructively proves that no ambiguity exists in the gluing of regional gauge-fixed configurations.
Time allowing I will also address how the formalism generalizes the “Dirac dressing” of charged matter fields, and how, in the presence of matter, quasi-local “global” charges (as opposed to gauge charges) emerge at special (i.e. reducible) configurations.

This talk is based on arXiv:1910.04222, with H. Gomes (U. of Cambridge, UK).
See also arXiv:1808.02074, with H. Gomes and F. Hopfmüller (Perimeter)

With the impressive number of binary black hole mergers observed by the LIGO-Virgo detector network in the recent years, it is now important to understand the formation channels of these systems. This talk focuses on the common envelope phase, crucial to the formation of compact object binaries. During this phase, the two companions evolve inside a shared envelope, with the secondary object orbiting towards the core of the primary star. Drag forces in the stellar envelope pull the two stellar cores into a tighter orbit. Additionally, the embedded object can be modified by accretion from the flow around it. I will present local simulations explaining the hydrodynamics of the common envelope inspiral phase, and highlight the effects of the full set of flow parameters on accretion and drag forces in these episodes. I will then discuss the transformation of binaries in common envelope phases and the effect of this phase on the properties of stellar-mass black hole populations

Historically, new particles and forces in the Standard Model have most often revealed themselves at high-energy particle colliders. Certain phenomena beyond the Standard Model, however, are best studied by using carefully designed low-energy precision measurements, or via their imprints on astrophysical and cosmological observables. In this talk, I will provide a concise overview of some of the new experiments and searches devised to look for new physics beyond the Standard Model. In particular, I will discuss recent developments in the new experimental and theoretical program of cosmological collider physics and how we can use the cosmological collider as a tool to study the structure of the Higgs potential at very high energies.

Quantizing 4D geometries leads to discrete area spectra. Such discrete area spectra are also suggested by the holographic principle and entropy counting for black holes.

 Starting with this input of a discrete area spectrum I will construct a path integral for quantum gravity and discuss (quantum) corrections to the GR dynamics that are forced by the discrete area spectra. The resulting model can serve as effective model for the spin foam approach and clarifies  the dynamical principles and underlying key assumptions for spin foams. The considerations also point towards key phenomenological differences to e.g. the ADM quantization scheme, and thus to a way to falsify the key assumption of discrete area spectra. 

Observations have shown that nearly all galaxies harbor massive or supermassive black holes at their centers. Gravitational wave (GW) observations of these black holes will shed light on their growth and evolution, and the merger histories of galaxies. Massive and supermassive black holes are also ideal  laboratories for studying strong-field gravity. Pulsar timing arrays (PTAs) use observations of millisecond pulsars to detect low-frequency GWs with frequencies ~1-100 nHz, and can detect GWs emitted by supermassive black hole binaries, which form when two galaxies merge. I will discuss source modeling and detection techniques for PTAs, as well as present limits on nanohertz GWs from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration.

Geometry of a pair of complex Lagrangian submanifolds of a complex symplectic manifold appears in many areas of mathematics and physics,  including exponential integrals in finite and infinite dimensions,  wall-crossing formulas in 2d and 4d, representation theory, resurgence of WKB series and so  on.

In 2014 we started a joint project with Maxim Kontsevich which we  named "Holomorphic Floer Theory" (HFT for short) in order to study all these (and other) phenomena as a part of a bigger picture.

Aim of my talk is to discuss  aspects of HFT related to deformation quantization of complex symplectic manifolds, including the conjectural Riemann-Hilbert correspondence.  Although some parts of this story have been already reported elsewhere, the topic has  many ramifications which have not been discussed earlier.

It is believed that active quantum error correction will be an essential ingredient to build a scalable quantum computer. The currently favored scheme is the surface code due to its high decoding threshold and efficient decoding algorithm. However, it suffers from large overheads which are even more severe when parity check measurements are subject to errors and have to be repeated. Furthermore, the number of encoded qubits in the surface code does not grow with system size, leading to a sub-optimal use of the physical qubits.

Finally, the decoding algorithm, while efficient, has non-trivial complexity and it is not clear whether it can be implemented in hardware that can keep up with the classical processing.

We present a class of low-density-parity check (LDPC) quantum codes which fix all three of the concerns mentioned above. They were first proposed in [1] and called 4D hyperbolic codes, as their definition is based on four-dimensional, curved geometries. They have the remarkable property that the number of encoded qubits grows linearly with system size, while their distance grows polynomially with system size, i.e. d~n a with 0.1 < a < 0.3. This is remarkable since it was previously conjectured that such codes could not exist [1]. Their structure allows for decoders which can deal with erroneous syndrome measurements, a property called single-shot error correction [2] as well as local decoding schemes [3].

Although [1] analyzed the encoding rate and distance of this code family abstractly, it is a non-trivial task to actually construct them. There is no known efficient deterministic procedure for obtaining small examples. Only single examples of reasonable size had been obtained previously [4]. These previous examples were part of different code families, so that it was not possible to determine a threshold. We succeeded to construct several small examples by utilizing a combination of randomized search and algebraic tools. We analyze the performance of these codes under several different local decoding procedures via Monte Carlo simulations. The decoders all share the property that they can be executed in parallel in O(1) time. Under the phenomenological noise model and including syndrome errors we obtain a threshold of ~5% which to our knowledge is the highest threshold among all local decoding schemes.

[1] A. Lubotzky, A. Guth, Journal Of Mathematical Physics 55, 082202 (2014).
[2] H. Bombin, Physical Review X 5 (3), 031043 (2015).
[3] M. Hastings, QIC 14, 1187 (2014).
[4] V. Londe, A. Leverrier, arXiv:1712.08578 (2017).

Idempotent (aka Karoubi) completion is used throughout mathematics: for instance, it is a common step when building a Fukaya category. I will explain the n-category generalization of idempotent completion. We call it "condensation completion" because it answers the question of classifying the gapped phases of matter that can be reached from a given one by condensing some of the chemicals in the matter system. From the TFT side, condensation preserves full dualizability. In fact, if one starts with the n-category consisting purely of ℂ in degree n, its condensation completion is equivalent both to the n-category of n-dualizable ℂ-linear (n-1)-categories and to an n-category of lattice condensed matter systems with commuting projector Hamiltonians. This establishes an equivalence between large families of TFTs and of gapped topological phases. Based on joint work with D. Gaiotto.