Talks

In this talk, I will discuss a new duality that was recently discovered in joint work with David Ayala and Nick Rozenblyum, which we refer to as reflection.

In essence, reflection amounts to two dual methods for reconstructing objects, based on a stratification of the category that they live in. As a classical example, an abelian group can be reconstructed on the one hand in terms of its p-completions and its rationalization, or on the other (reflected) hand in terms of its p-torsion components and its corationalization; and these both come from a certain "closed-open decomposition" of the category of abelian groups.

Examples and applications of reflection are abundant, because stratifications are abundant. In algebra, reflection recovers the derived equivalences of quivers coming from BGP reflection functors (hence the terminology "reflection"). In topology, reflection is closely related to Verdier duality, a generalization of Poincaré duality that applies to singular spaces. Moreover, an explicit description of reflection leads to a categorification of the classical Möbius inversion formula, a Fourier inversion theorem for functions on posets.

Zoom Link: https://pitp.zoom.us/j/92439401154?pwd=cGZsUGJGcmNXdFZuclREL3gyYnhQdz09

The vast and growing number of publications in all disciplines of science cannot be comprehended by a single human researcher. As a consequence, researchers have to specialize in narrow subdisciplines, which makes it challenging to uncover scientific connections beyond the own field of research.

In my talk, I will present a possible solution: I demonstrate the development of a semantic network for quantum physics (SemNet), using 750,000 scientific papers and knowledge from books and Wikipedia. I use it in conjunction with an artificial neural network for predicting future research directions. Finally, I show first indications how individual scientists can use SemNet for suggesting and inspiring personalized, out-of-the-box ideas.

I believe that computer-inspired scientific ideas will play a significant role in accelerating scientific progress, and am looking forward hearing your thoughts and ideas about this crucial question.

References
[1] Mario Krenn, Anton Zeilinger, Predicting research trends with semantic and neural networks with an application in quantum physics, PNAS 117(4) 1910-1916 (2020).
[2] IEEE BigData 2021 competition: Science4Cast: https://github.com/iarai/science4cast

Zoom Link: https://pitp.zoom.us/j/92240839439?pwd=LytUTHlMWE9ycjlsUXJkdHRta2c1UT09

Over the next ten years, the Vera C. Rubin Observatory (VRO) will observe ∼10 million active galactic nuclei (AGN) with a regular and high cadence. During this time, the intensities of most of these AGN will vary stochastically. Moreover, these fluctuations may also be connected to the high-energy astrophysical neutrino (HEAN) flux observed by IceCube. In this talk, I explore the prospects to quantify these fluctuations with VRO-measurements of AGN light curves and also evaluate the capacity of VRO, in tandem with various current and upcoming neutrino telescopes, to establish AGN as HEAN emitters.  I find that AGN variability measurements will be so precise as to allow the AGN to be separated into up to ∼ 10 different correlation-timescale bins. I also show that if the correlation time varies as some power of the luminosity, the normalization and power-law index of that relation will be determined to O(10^{−4}%).  Finally, I find that it may be possible to detect AGN contributions at the ~ 3\sigma level to the HEAN flux even if these AGN contribute only ~10% of the HEAN flux.
 

The charge resistivity/conductivity can take universal values in various scenarios of two-dimensional condensed matter systems. Well-known examples of universal resistivity include 2+1d quantum critical points, (fractional) quantum Hall effects, the criterion of two-dimensional “bad metal”, and the universal resistivity jump predicted at the interaction-driven metal-insulator transition. We construct examples of two-dimensional metallic states with the following exotic behaviors: (1) at low temperature this state is a “bad metal” whose resistivity can be much larger than the Mott-Ioffe-Regel limit; (2) while increasing temperature T the resistivity ρ(T) crosses over from a bad metal at low T to a good metal at intermediate T; (3) at low temperature the metallic state has a large Lorenz number, which strongly violates the Wiedemann-Franz law; (4) the state also has a large thermopower (Seebeck coefficient). Motivated by the recent experiment in transition metal dichalcogenides, an exotic interaction-driven metal-insulator transition will also be constructed. The universal resistivity jump at this transition far exceeds what was proposed in previous theory.

Zoom Link: https://pitp.zoom.us/j/93625929658?pwd=Y284ZTZpWFM1RnduSmhXdDZBRjgyQT09

I study the dynamics of a gyroscope far from an isolated source of gravitational waves. With respect to a local frame 'tied to the distant stars', the gyroscope precesses when gravitational waves cross its path, resulting in a net `orientation memory', carrying information on the gravitational wave profile. I show that the precession rate is given by the so-called "dual covariant mass aspect", providing a celestially local measurement protocol for this quantity. Moreover, I show that the net memory effect can be derived from the flux-balance equations for superrotation charges in the "generalized BMS" algebra. Finally, I show how the spin memory effect à la Pasterski et al. is reproduced as a special case.

Fractons are relatively new types of quasiparticles which have recently been inspiring activity within several branches of physics. I will offer some motivations and perspectives from quantum information theory, condensed matter physics, and high energy physics, focusing mainly on my work in the latter two subjects. This talk is primarily based on https://arxiv.org/abs/2108.08322 and a paper to appear shortly with Dominic Williamson.

Guided by the principles of effective field theory (EFT), I will discuss three avenues to constrain physics beyond General Relativity with black-hole observations.

1) Shadows: Without specifying any particular gravitational dynamics, I will discuss image features of black-hole shadows in general parameterizations and their relation to fundamental-physics principles like (i) regularity (no remaining curvature singularity), (ii) simplicity (a single new-physics scale), and (iii) locality (a new-physics scale set by local curvature).

2) Stability: Specifying the linearized dynamics around black-hole spacetimes determines the onset of potential instabilities and connects to the ringdown phase of gravitational waves. I will delineate how said instabilities can constrain the EFT of gravity, theories of low-scale dark energy, as well as ultralight dark matter.

3) Nonlinear evolution: The larger the probed curvature scale, the tighter the constraints on new gravitational physics. Making full use of experimental data, thus relies on predictions in the nonlinear regime of binary mergers. I will present recent progress towards achieving stable numerical evolution for the EFT of gravity up to quadratic order in curvature.

Zoom Link: https://pitp.zoom.us/j/98276687334?pwd=UnM2dElacWNtempQUHJMNVlaNHgyUT09

Conformal field theories have played an important role in understanding the origin of gravitational entropy, as the Cardy formula accounts for the entropy of three-dimensional BTZ black holes or black holes with an AdS3 near-horizon region. More recently, Cardy-type formulas have also been derived for different field theories, such as warped conformal field theories, which are two-dimensional field theories invariant under chiral scaling symmetry.

In this talk I discuss a particular class of three-dimensional spacetimes, dubbed warped flat spaces. I will present their geometric and thermodynamic properties, focusing on their causal structure. I will explain how their entropy can be accounted for through a dual description in terms of a warped conformal field theory.

When an interacting quantum many-body system is cooled down to its ground state, there can be discrete "topological invariants" that characterize the properties of such ground states. This leads to the concept of "topological phases of matter" distinguished by these topological invariants. Experimental manifestations of these topological phases of matter include the integer and fractional quantum Hall effect, as well as topological insulators.

In this talk, after a general overview of topological phases of matter, I will explain how to define topological invariants that are specific to the ground states of regular crystals, i.e. systems that are periodic in space. I will discuss the physical manifestations of the resulting "crystalline topological phases", including implications for the properties of crystalline defects such as dislocations and disclinations. Then, I will explain how these ideas can be generalized to quasicrystals, which are a different class of materials that have long-range spatial order without exact periodicity. These ideas ultimately lead to a general classification principle for crystalline and quasicrystalline topological phases of matter.

Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the state to the measurement basis. However, it is quite challenging to realize deep unitary circuits on near-term quantum devices, and an unbiased reconstruction map is non-trivial to find for arbitrary random unitary ensembles. In this talk, I will discuss our recent progress on combining classical shadow tomography with quantum chaotic dynamics. Particularly, I will introduce two new families of shadow tomography schemes: 1) Hamiltonian-driven shadow tomography and 2) Classical shadow tomography with locally scrambled quantum dynamics. In both works, I’ll derive the unbiased reconstruction map, and analyze the sample complexity. In the Hamiltonian-driven scheme, I will illustrate how to use proper time windows to achieve a more efficient tomography. In the second work, I will demonstrate advantages of shadow tomography in the shallow circuit region. Then I’ll conclude by discussing approximate shadow tomography with local Hamiltonian dynamics, and demonstrate that a single quench-disordered quantum spin chain can be used for approximate shadow tomography.

References:
[1] Hong-Ye Hu, Yi-Zhuang You. “Hamiltonian-Driven Shadow Tomography of Quantum States”. arXiv:2102.10132 (2021)
[2] Hong-Ye Hu, Soonwon Choi, Yi-Zhuang You. “Classical Shadow Tomography with Locally Scrambled Quantum Dynamics”. arXiv: 2107.04817 (2021)

Zoom Link: https://pitp.zoom.us/j/99011187936?pwd=OVU3VkpyZ21YcXRCOW5DOHlnSWlVQT09