Scientific Series

In the last few years there have been demonstrations of quantum advantage using noisy quantum circuits that are believed to go beyond the limits of the classical computers that exist today.  In this talk I will give an overview of a different type of quantum advantage that can be attained by shallow (short-depth) quantum circuits.  I will discuss recent results which establish unconditionally that constant-depth quantum circuits can solve certain linear algebra problems faster than their classical counterparts. We will see that the reason quantum computers solve these problems provably faster (as measured by circuit depth) than classical computers is due to a strong form of quantum nonlocality that is present in their input/output statistics. 

Zoom Link: https://pitp.zoom.us/j/96752851897?pwd=R29GWHovN0MwVXVYWklaNE1QZ1c5dz09

Multi-matrix integrals in  planar, large N limit are genuine functional integrals, in general very difficult to compute.  Apart from some known solvable examples (one-matrix model, two-matrix model with specific interaction, etc) one has to rely on perturbation theory or Monte-Carlo at large enough N.  Matrix bootstrap (MB), initiated by Anderson and Kruczenski, and Lin,  is an interesting alternative to these methods. MB deals with the planar loop equations for loop moments -- the averages of traces of "words" built out of products of matrix variables.   The number of unknowns - loop moments - grows with the length of words quicker then the number of  loop equations. The needed extra conditions come from the positivity of correlation matrix of loop moments. This allows, at a given cut-off on the length of words, to establish the upper and lower limits for particular, lowest loop moments, sometimes with an excellent precision.  The main difficulty of the previous works is the non-linearity of loop equations, leading to a  non-convex  optimization procedure. In our recent paper with Zechuan Zheng, we propose to complete this scheme with the relaxation procedure:   the non-linear loop equations are incorporated into the relaxation matrix  as linear inequalities. The problem becomes the standard SDP, allowing for longer loops and thus a better precision. We demonstrate the relaxed matrix bootstrap (RMB) on the example of an analytically unsolvable 2-matrix model. The RMB for Z_2 symmetric states  gives a very satisfactory precision for generic parameters,  up to 6 digits.  We also managed  to apply   RMB  to  more challenging, Z_2 symmetry breaking solutions, though with  less of precision.  We also prove analytically, using the Hamburger problem, that MB for the 1-matrix model converges to physical solutions, with eigenvalues distributed only on the real axis.

 The existence of right-handed neutrinos may shed light on the origin of neutrino masses. It is also conceivable that if these particles exist, they may have a new set of interactions and symmetries of their own. In this talk, I will discuss "lamppost" models where MeV to GeV heavy neutrinos interact with a dark photon, and discuss some novel experimental signatures at neutrino detectors, e+e− colliders, and kaon decays. I will also comment on some connections to MiniBooNE and the (g-2) of the muon.

In this talk, I will present recent results about gravitational wave cosmology. I will argue that the spatial clustering of gravitational wave sources provides a wealth of invaluable information concerning the origin of binary black holes and the propagation law of gravitational waves. The former can clarify whether the observed black hole binaries are of stellar or primordial origin. The latter is important for constraining deviations from General Relativity on cosmological scales because such deviations predict modified propagation of gravitational waves compared to General Relativity. I will then explore the possibility of observed black holes having primordial origin and present its consequences for expected merger rates of such black holes and neutron stars. Time permitting, I will also summarize our recent progress made in the field of primordial gravitational waves and the implications for the inflationary models.

The program of Ben-Zvi--Sakellaridis--Venkatesh connects the construction of L-functions in number theory with S-duality of boundary conditions in 4d. In particular this predicts certain equivalences of categories between equivariant D-modules on the formal loop space of a smooth variety X and equivariant quasi-coherent sheaves on a Hamiltonian manifold. I discuss an extension of this conjecture to certain singular varieties X and the possibility of quantizing the equivalence. I will explain joint work with Yiannis Sakellaridis on computing a certain factorization algebra which plays a role in the story. 

Zoom Link: https://pitp.zoom.us/j/95543248994?pwd=bmZIRnEyLzZnNmlEWW5oNTEwaEhNUT09

This talk is devoted to the geometric approach to supergravity and applications in the framework of loop quantum gravity. Among other things, this approach leads to a reformulation of the theory in which (part of) supersymmetry manifests itself in terms of a gauge symmetry. Using the interpretation of supergravity in terms of a super Cartan geometry, we will derive the Holst variant of the MacDowell-Mansouri action for N=1 and N=2 AdS supergravity in D=4 for arbitrary Barbero-Immirzi parameters. We will show that these actions provide unique boundary terms that ensure local supersymmetry invariance at boundaries. The chiral case is special. The action is invariant under an enlarged gauge symmetry, and the boundary theory is a super Chern-Simons theory. The action also implies boundary conditions that link the super electric flux through, and the super curvature on, the boundary. Applications we have in mind are supersymmetric black holes and loop quantum cosmology. To this end, we will study a class of symmetry reduced models of chiral supergravity. The enlarged gauge symmetry of the chiral theory is essential as it allows for nontrivial fermionic degrees of freedom even if one imposes spatial isotropy. The quantization of the theory yields a natural state space and allows a consistent implementation of the constraint algebra.

Finally, we will give an outlook on applications towards a quantum description of supersymmetric black holes in the context of LQG and possible relations to superstring theory.

In the first half of this talk I will discuss recent developments in Gamma Ray Burst (GRB) afterglows.  GRBs associated with gravitational wave events are, and will likely continue to be, viewed at a larger inclination than GRBs without gravitational wave detections.  Viewing GRBs and their afterglows at large inclination can massively affect the observed electromagnetic emission. I will discuss how we model and reason about GRB afterglows in this new era, and new software tools to aid in this work. With our theoretical tools in hand we will briefly go over some recent applications of these models to both short and long GRBs.

In the second half of this talk I will cover ongoing work on binary black hole accretion with the moving-mesh hydrodynamics code Disco.  Gas accretion may hinder or accelerate the merger of supermassive binary black holes, affecting predicted rates for LISA and PTA targets.  Determining the magnitude and sign of the torque exerted on the black hole binary by surrounding gas is a difficult problem that can only be approached by hydrodynamic simulation.  I will discuss recent simulations with Disco that explore the dependence of this torque on the mass ratio of the binary and temperature of the gas, the latter of which can reverse the sign of the torque.

In 1930, the famous statistician and geneticist Ronald Fisher claimed to have proved a "fundamental theorem of natural selection". He compared this result to the second law of thermodynamics, and described it as holding "the supreme position among the biological sciences". But others found it obscure, and in its most obvious interpretation it is simply false. Luckily there is a true result closely resembling Fisher's claim: a general theorem connecting dynamical systems and information theory. I'll explain this, give the very simple proof, and draw a few conclusions.

Zoom Link: https://pitp.zoom.us/j/99898585189?pwd=NytLaWt2RjFPOTVJOEptMlBBd1BvZz09

I will discuss a set of calculations of dark matter interactions with low threshold semi-conductor detectors such as SENSEI and superCDMS. As a warm-up, I'll show how to rephrase traditional DM-electron scattering calculations in terms of the energy loss function of the material. We will then apply this framework to compute the rate for the Migdal effect in semi-conductor targets. This is needed because the traditional calculations of the Migdal effect do not apply in low threshold semi-conductor detectors, as the delocalized nature of the valence electrons is not taken into account.

Although cold dark matter (CDM) has been established, this is only the case for measurements at large scales, which are larger than galaxy-sized structures. Even though we need to understand the important role of baryonic components, matter distribution at small scales can be the key to distinguishing different particle dark matter candidates. In fact, warm dark matter, self-interacting dark matter, and fuzzy dark matter have been proposed, yielding different matter distributions at sub-galactic scales. These small-scale distributions have been studied with numerical simulations. Whereas very reliable, numerical simulations suffer certain issues. They are limited by both numerical resolution and shot noise. They tend to take a lot of computational time. These might be a bottleneck for surveying through multi-dimensional parameter space of various dark matter models. I present semi-analytic models of small-scale structure, especially dark matter subhalos, which are based on structure formation theory and the tidal evolution of subhalos. Our models for CDM have been well tested against the results of various numerical simulations. The semi-analytic models are free from all the problems of the numerical simulations mentioned above. Therefore, they might be essential ingredients for identifying the particle nature of dark matter through gravitational (lensing, pulsar timing), astrophysical (satellite counts, stellar streams), and astroparticle probes (gamma rays).

The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown that this model exhibits a symmetry under the (2+1)-dimensional Poincaré group. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. It also unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior. Remarkably, the physical ISO(2,1) symmetry can be seen as a broken infinite-dimensional symmetry. This is done by reinterpreting the action for the model as a geometric action for the BMS3 group, where the configuration space variables are elements of the algebra bms3 and the equations of motion transform as coadjoint vectors.

Zoom Link: https://pitp.zoom.us/j/99646733321?pwd=U05kYU85V0Q4VCtrZ1BNV2JZbE1DUT09