Scientific Series

The angular resolution of a stellar interferometer, as for a single telescope, becomes better at smaller wavelengths and larger baselines. The goal for ground detectors would then be optical interferometers with baselines as long as the Earth’s diameter. The latter goal has been achieved in radio, but it becomes prohibitive in the optical, as the electromagnetic field oscillates too rapidly to record and analyze directly over km-long baselines. Intensity interferometry relying on second-order correlations can make this possible: rather than the amplitude and phase of incoming light, we need only count photons. This technique has a long history and to date the best measurements of nearby stellar radii, dating back to the 1950s. Its main limitations are the need for very bright sources and its narrow field of view, restricting kilometer-long baselines to sources only a few μas away. In this talk, I will propose an optical-path modification of astronomical intensity interferometers, which introduces an effective time delay in the two-photon interference amplitude, splitting the main intensity correlation fringe into others at finite opening angles, allowing for differential astrometry of multiple compact sources such as stars or quasar images. Together with the exponential progress in the field of single photon detection, such a modification will immensely increase the scope of intensity interferometry beyond measurements of the optical emission region morphology. I will lay out the theory and technical requirements of time-delay intensity interferometry and, time permitting, I will talk about some promising applications, which include astrometric microlensing of stars and quasar images, binary-orbit characterization, exoplanet detection, Galactic acceleration measurements and calibration of the cosmic distance ladder, all at unprecedented relative astrometric precision.

Zoom Link: TBD

The recent advancement of machine learning provides new opportunities for tackling challenges in quantum science, ranging from condensed matter physics, high energy physics to quantum information science. In this talk, I will first discuss a class of anti-symmetric wave functions based on neural network backflow,  which is efficient for simulating strongly-correlated lattice models and artificial quantum materials. Next, I will talk about recent progress of simulating continuum quantum field theories with neural quantum field state, and lattice gauge theories such as 2+1D quantum electrodynamics with finite density dynamical fermions using gauge symmetric neural networks. I will further discuss neural network representation based on positive-value-operator and phase space measurements for quantum dynamics simulations. Finally, I will present applications of machine learning in quantum control, quantum optimization and quantum machine learning.

Zoom link:  https://pitp.zoom.us/j/93834456412?pwd=R0hxdEpxanFFRnZmTHlqZTBXRi82QT09

I will describe a general categorical approach to constructing Hamiltonian actions on moduli spaces. In particular cases, this specializes to give a ``universal" Hitchin integrable system as well as the Calogero-Moser system.  Moreover, I will describe a generalization to higher dimensions of a classical result of Goldman which says that the Goldman Lie algebra of free loops on a surface acts by Hamiltonian vector fields on the character variety of the surface.  A key input is a description of deformations of Calabi-Yau structures, which is of independent interest. This is joint work with Chris Brav.

Zoom link:  https://pitp.zoom.us/j/92929253744?pwd=WGFNQmRJck5NdzFFdU8xcXRlN3RRQT09

The geometry of kilonovae is a key diagnostic of the physics of merging neutron stars with current hydrodynamical merger models typically showing aspherical ejecta. Previously, Sr II was identified in the spectrum of the only well-studied kilonova AT2017gfo, associated with the gravitational wave event GW170817. In this talk, we show that combining the strong Sr II P Cygni absorption-emission spectral feature and the blackbody nature of the kilonova spectrum, to determine that the kilonova is highly spherical at early epochs. Line shape analysis combined with the known inclination angle of the source also shows the same sphericity independently. The near-spherical geometry suggests early spectra of kilonovae may provide excellent precision cosmic distance measurements using the Expanding Photosphere Method.

Zoom link:  https://pitp.zoom.us/j/97287055430?pwd=bFVyeTRuZHVLcGlDdnhlK1d0OWE1Zz09

There is a by now standard procedure for calculating twisted spin, spin^c, and string bordism groups for applications in physics: realize the twist as arising from a vector bundle, which allows one to split the corresponding Thom spectrum and greatly simplify the Adams spectral sequence computation. Not all twists arise from vector bundles, but Matthew Yu and I noticed that if you ignore this fact and pretend that everything is OK, you still get the right answer! In this talk, I'll discuss a theorem Matthew and I proved explaining this, by calculating the input to Baker-Lazarev's version of the Adams spectral sequence. Then I will discuss applications to anomalies of some quantum field theories and supergravity theories.

Zoom link:  https://pitp.zoom.us/j/93508575689?pwd=YVV6VlRwL1RGSG55V0cwTzdpUWROUT09

In this colloquium, I will review how the notion of quantum error-correction has transformed our understanding of quantum gravity in the past decade.

Zoom link:  https://pitp.zoom.us/j/94349082665?pwd=OFdJdkpHU1NEcmlNeW5pWlg4WmNBZz09

Scattering amplitudes are where quantum field theory directly meets collider experiments.  An excellent model for scattering in QCD is provided by N=4 super-Yang-Mills theory, particularly in the planar limit of a large number of colors, where the theory becomes integrable.  The first nontrivial amplitude in this theory is for 6 gluons.  It can be computed to 7 loops using a bootstrap based on the rigidity of the function space of multiple polylogarithms, together with a few other conditions.  One can also bootstrap a particular form factor, for the chiral stress-tensor operator to produce 3 gluons, through 8 loops.  This form factor is the N=4 analog of the LHC process, gluon gluon --> Higgs + gluon. Remarkably, the two sets of results are related by a mysterious `antipodal' duality, which exchanges the role of branch cuts and derivatives.  Furthermore, this duality is `explained' by an antipodal self-duality of the 4 gluon form factor of the same operator; although it is still fair to say of the self-duality, `who ordered that?'

Zoom link:  https://pitp.zoom.us/j/96265005656?pwd=Qndza3pIKzdmZVJGL0s1ZUZkRmp4QT09

Precision measurements of primordial correlators in the CMB, Large Scale Structure, and 21-cm cosmology may contain “on-shell" imprints of extremely heavy particle physics, with masses comparable to the inflationary Hubble scale, via the remarkable inflationary mechanism known as “cosmological collider physics”. I will describe my research in (a) finding new robust mechanisms for extending the energy range and strength of such signals, (b) identifying motivated particle physics targets that may be discoverable, (c) showing how cosmological collider physics can probe the mechanism of inflation itself, and (d) demonstrating variants of the mechanism that may be observable in new cosmological “maps”, such as stochastic gravitational wave backgrounds with significant anisotropies. While this is an ambitious program of research, there are major challenges to bring it to fruition, on the experimental, phenomenological and theoretical fronts, which I will sketch. 

Zoom Link:  https://pitp.zoom.us/j/98923687484?pwd=cjgweEhoejVCeHAvc0RBSDEvVkZldz09

There are numerous properties of quantum states that one might be interested in characterizing, including statistical moments of observables such as expectations or variances, or more generally purities, entropies, probabilities, eigenvalues, symmetries, marginals, etc. Given a fixed collection of properties, the realizability problem aims to determine which value-assignments to those properties are jointly exhibited by at least one quantum state. In addition to the decision problem of realizability, one might also be interested in quantifying what proportion of quantum states possesses those property values. 

Any property of a quantum state can always, at least in principle, be estimated empirically by suitably measuring an ensemble of many independently and identically prepared copies of that quantum state. The particular sequence of positive operator valued measures which estimates a given property is known as a property estimation scheme. The purpose of this talk is to discuss a strategy for tackling realizability problems by studying the large deviation behaviour of property estimation schemes.

The key idea of this approach is the following:
A given collection of properties is realized by a quantum state if and only if a random quantum state occasionally produces that collection of properties as estimates.
Under suitable conditions, this observation leads to a complete hierarchy of necessary conditions for realizability.

Zoom link:  https://pitp.zoom.us/j/91945653382?pwd=QTZqSnpjYjlxYndqaHZwN2lES1h1Zz09

 I will present a novel behavior developed by scattering amplitudes in certain regions of the kinematic space, in which amplitudes factorize into 3 pieces without becoming singular. This is opposed to what happens in standard factorization or soft limits. We call this behavior a 3-split, and it is "semi-local" in nature. As 3-splits cannot be obtained from standard unitarity arguments, they represent a new phenomenon in QFT. I will introduce 3-splits in their simplest version, i.e. for the biadjoint scalar theory (which I will also introduce). If time allows, I will also comment on how 3-splits arise in other QFTs and how they lead to the discovery of more general theories.

Zoom link:  https://pitp.zoom.us/j/95575818902?pwd=V1RKYW9WMmZQNElVL2VyUGFGMFgxQT09

The angular resolution of a stellar interferometer, as for a single telescope, becomes better at smaller wavelengths and larger baselines. The goal for ground detectors would then be optical interferometers with baselines as long as the Earth’s diameter. The latter goal has been achieved in radio, but it becomes prohibitive in the optical, as the electromagnetic field oscillates too rapidly to record and analyze directly over km-long baselines. Intensity interferometry relying on second-order correlations can make this possible: rather than the amplitude and phase of incoming light, we need only count photons. This technique has a long history and to date the best measurements of nearby stellar radii, dating back to the 1950s. Its main limitations are the need for very bright sources and its narrow field of view, restricting kilometer-long baselines to sources only a few μas away. In this talk, I will propose an optical-path modification of astronomical intensity interferometers, which introduces an effective time delay in the two-photon interference amplitude, splitting the main intensity correlation fringe into others at finite opening angles, allowing for differential astrometry of multiple compact sources such as stars or quasar images. Together with the exponential progress in the field of single photon detection, such a modification will immensely increase the scope of intensity interferometry beyond measurements of the optical emission region morphology. I will lay out the theory and technical requirements of time-delay intensity interferometry and, time permitting, I will talk about some promising applications, which include astrometric microlensing of stars and quasar images, binary-orbit characterization, exoplanet detection, Galactic acceleration measurements and calibration of the cosmic distance ladder, all at unprecedented relative astrometric precision.

Zoom link:  https://pitp.zoom.us/j/92041231568?pwd=cWo2c0hwTEdmOTRCc042SHNxRWw5UT09

On smooth schemes, every coherent sheaf admits a finite resolution by vector bundles, but on singular schemes, this is no longer true. The Arinkin-Gaitsgory singular support of coherent sheaves is an invariant of coherent sheaves on certain singular spaces that measures how far a particular coherent sheaf is from having such a resolution. In this talk, I will explain how the Arinkin-Gaitsgory theory of singular support decategorifies to a notion of singular support for chains on the associated complex analytic space of our scheme, measuring the difference between cohomology and Borel-Moore homology on singular spaces. In order to do so, we take advantage of the relationship between coherent sheaves and certain categories of matrix factorizations, also know as D-branes in Landau-Ginzburg models.

Zoom link: https://pitp.zoom.us/j/95698955865?pwd=Rm9ld3FUK3hiWGUzenBuZnQyTTRYZz09