Scientific Series

The (derived) geometric Satake equivalence plays a central role in the geometric Langlands program: roughly, it describes the category of constructible sheaves of C-vector spaces on Bun_G(S^2) in terms of the Langlands dual group G^. In this talk, I will describe some ideas connecting chromatic homotopy theory to the derived geometric Satake equivalence. For example, we will describe the category of locally constant sheaves of A-modules on Bun_G(S^2), where A is complex K-theory or an elliptic cohomology theory, in Langlands
dual terms. Some of this work was motivated by considerations from physics, and I hope to say what little I know about this, as well as sketch its relationship to the Ben-Zvi-Sakellaridis-Venkatesh program.

Zoom Link:  https://pitp.zoom.us/j/94926220665?pwd=bVZFUFlvZGxVSG0xUFc1SGNaTDBKZz09

Chern-Simons theories can possess 't Hooft anomalies for time-reversal symmetry. In this talk, we will discuss abelian Chern-Simons theories with an interesting time-reversal symmetry algebra and compute the classification of the anomaly, which is captured by a bordism group. In order to get the classification correct I will explain the argument we used that utilized the Smith homomorphism for bordism groups. In order to compute the value of the anomaly we study the Atiyah-Hirzebruch spectral sequence and find a way to trivialize each layer of the anomaly. I will also discuss the generating manifold for the corresponding bordism group, and how it arises from the Smith homomorphism. The knowledge of this manifold allows one to compute the partition function by using the data that characterizes the Chern-Simons theory and the symmetry actions; this gives a robust check of our answer for the anomaly. This is based on work in progress with Arun Debray and Weicheng Ye. 

Zoom link:  TBA

 I will talk about new constructions to the parity-violating sector of gravity that can yield large observables, in particular those from inflation. Within this framework, I will demonstrate the potential for seeking gravitational parity-violation in  uncharted regions of parameter space and give hints to novel methods of probing baryogenesis. I will also comment on a few interesting theoretical aspects regarding inflationary  correlators.

Zoom link:  https://pitp.zoom.us/j/95924890817?pwd=MkRyWmV2a3g1dndPNFhoVlQvb3Ixdz09

After discussing the basics of Carrollian physics, we shall revisit the motion  of massless particles with anyonic spin in the black hole horizons. As recently shown, such particles can move within the horizon of the black hole due to the  coupling of charges associated with a 2-parametric central extension of the 2-dimensional Carroll group to the magnetic field around the black hole -- the so called "anyonic  spin-Hall effect". We shall study several examples of such motions. Of these, the most  interesting is the motion in misaligned (asymptotically uniform) magnetic field around Kerr,  which results in a time dependent motion of Carrollian particles that is reminiscent  of "monarch migration".

Zoom link:  https://pitp.zoom.us/j/97094479078?pwd=SHN6NEU5aE93OXVQYk9aWTVOdzRRUT09

Cluster structure on a quantum group allows one to work with its positive representations, a special class of modules similar in spirit to principal series representations but closed under tensor multiplication. On the other hand, cluster techniques proved inadequate for the study of finite-dimensional representation theory. I will discuss how one can reconcile positive and finite-dimensional representations into one theory by studying moduli spaces of local systems with non-generic monodromies.

Zoom link:  https://pitp.zoom.us/j/97677905324?pwd=Tkxlei9wN1llYVpncHA2cnpYKzlhUT09

Dynamical fixed points are late-time attractors of interactive QFTs that differ from thermal equilibria by a constant entropy production rate. We use holographic framework to analyze such fixed points of strongly coupled gauge theories, driven by homogeneous and isotropic expansion of the background metric - equivalently, a late-time dynamics of a corresponding QFT in Friedmann-Lemaitre-Robertson-Walker Universe. As an application, we discuss gravitational reheating of quark-gluon plasma in the exit from the early-cosmology inflation.

Zoom link:  https://pitp.zoom.us/j/96385064629?pwd=NTZrdUdtbW0rZkxPdFZ3ZnZRUzhjZz09

I will discuss a novel search for axions using spectropolarimetric observations of magnetic white dwarfs (MWDs). Photons produced as thermal radiation at the MWD surface may convert into an axion as they traverse the magnetosphere, but only the component polarized parallel to the MWD magnetic field. Therefore the MWD radiation at Earth is linearly polarized perpendicular to the magnetic field direction. I detail the analysis of archival linear polarization spectra of a few nearby MWDs that excludes the axion interpretation of the TeV gamma-ray transparency anomalies. I briefly discuss the sensitivity of ongoing and future searches using dedicated data at the Lick Observatory.

Zoom Link:  https://pitp.zoom.us/j/97657182582?pwd=ZlFYWWtoYXhQZUtnOUxsZFpqMUo1Zz09

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