Scientific Series

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

Symplectic duality predicts that symplectic singularities should come in pairs. For example, Nakajima quiver varieties are conjecturally dual to BFN Coulomb branches (of the corresponding quiver theories). Another family of potentially symplectically dual pairs was described recently in the works of Losev, Mason-Brown, and Matvieievskyi: they describe symplectically duals to Slodowy slices to nilpotent orbits.

In this talk, we will discuss the Hikita-Nakajima conjecture that relates the geometry of symplectically dual varieties. We will restrict to the cases of certain quiver varieties and Slodowy slices and discuss the picture in these cases.

Based on the joint work with Pavel Shlykov (arXiv:2202.09934) and the work in progress with Do Kien Hoang and Dmytro Matvieievskyi.

Zoom link:  https://pitp.zoom.us/j/98651907502?pwd=ODA1K3NKVHFLdkp6TEtaSnJXdThVZz09

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity.  Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes.  These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory  Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.  Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge mode

Zoom link:  https://pitp.zoom.us/j/98275430953?pwd=TzdTUXIvVWU4Ym1jcWRWbkgxZnhMdz09

Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the spurious topological entanglement entropy. We show this spurious contribution is always nonnegative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE which is invariant under constant-depth quantum circuits.

Based on a joint work with Daniel Ranard (MIT), Michael Levin (U Chicago), Ting-Chun Lin (UCSD), and Bowen Shi (UCSD)

Zoom link:  https://pitp.zoom.us/j/93809342984?pwd=QXJkK0ZYR3QzdjlUUWlkMEFXMWRnQT09

In massless QED, we find that the classical U(1) axial symmetry is not completely broken by the Adler-Bell-Jackiw anomaly. Rather, it is resurrected as a generalized global symmetry labeled by the rational numbers. Intuitively, this new global symmetry in QED is a composition of the naive axial rotation and a fractional quantum Hall state. The conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra. We further generalize our construction to QCD, and show that the neutral pion decay can be derived from a matching condition of the non-invertible global symmetry. Finally, we find a non-invertible Gauss law in axion-Maxwell theory.

Zoom link:  https://pitp.zoom.us/j/93832561140?pwd=czFFSkVvYS9RbXRjOTJPQVFhL2hGZz09

For more than a decade, enigmatic extragalactic flashes called fast radio bursts (FRBs) have defied a definitive explanation for their origin. In addition, the unique properties of FRBs make them promising probes of both cosmology and the distribution of gas on intergalactic scales. The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is the only radio telescope capable of instantaneously observing hundreds of square degrees with the sensitivity of a 100-meter scale aperture. As a result, its transient search instrument, CHIME/FRB, has detected thousands of FRBs, increasing the known sample by an order of magnitude. I will give an overview of CHIME/FRB's most recent results, where observations of particular sources and statistical analyses of the FRB population are starting to reveal the nature of this mysterious phenomenon. I will then describe an effort to augment CHIME/FRB's capabilities by adding Outrigger telescopes, which will be located across North America and will precisely localize FRB sources using very long baseline interferometry. The resulting large sample of localized FRBs will allow for detailed measurements of the large-scale distribution of baryons in the universe, providing precise constraints on feedback processes in galaxy evolution.

Zoom link:  https://pitp.zoom.us/j/93157775112?pwd=bzZDMVc3VnF1WHZzeVlLOTdDZmtQQT09

Every time researchers have pushed the energy boundary in particle physics we have found something new about our Universe. Recently, IceCube has demonstrated that Neutrino Telescopes can use neutrinos from the cosmos as excellent tools to continue this exploration. The true potential of this field, however, remains to be realized due to limited observations of neutrinos at the highest energies. To unlock this potential, advanced detectors are needed that will push the forefront of the cosmic frontier, revealing new knowledge of extreme astrophysical phenomena, including through multi-messenger follow-up programs, and testing fundamental physics at scales well beyond those reachable by Earth-bound accelerators. The Pacific Ocean Neutrino Experiment (P-ONE) is a proposed initiative to construct one of the largest neutrino telescopes deep in the northern Pacific Ocean off the coast of British Columbia. To overcome the challenges of a deep-sea installation, we have deployed two pathfinder mooring lines STRAW and STRAW-b in 2018 and 2020. These provide continuous monitoring of optical water properties at a potential detector site in the Pacific. In this talk I will cover results from these pathfinders and discuss the status of P-ONE. 

Zoom Link:  https://pitp.zoom.us/j/91718716984?pwd=Wm00anU4UjFWd0tKYVZ0TVZ6aVMrZz09

In quantum many-body physics, we aim to understand and predict the exciting phenomena emerging from the interactions of many quantum particles. In this talk I will use the paradigmatic Fermi-Hubbard model, a conceptually simple model of interacting fermionic particles, as an example to highlight different approaches to gain insights into quantum many-body problems. I will describe a semi-analytical theory, established numerical methods, machine learning techniques, as well as quantum simulation experiments, which provide detailed information about the quantum state of the system. A particular focus will be on how to combine these different approaches to learn as much as possible about the system of interest, for example through new observables and modified microscopic models.

Zoom link:  https://pitp.zoom.us/j/94368447256?pwd=clhQcUJNaTR0UjVydnBHelo4N3JIQT09

The rich interplay between three-dimensional topological quantum field theories (TQFTs) and vertex operator algebras (VOAs) has been a useful bridge in understanding aspects of both subjects. In this talk, I will describe some aspects of this correspondence focusing on the simple, yet surprisingly rich, examples of Chern-Simons theories based on the Lie superalgebra gl(1|1).

Zoom Link:  https://pitp.zoom.us/j/97698409749?pwd=ZkdzUHI2YXJEYk53VDQyZm1ERzJHUT09

Generative modeling via diffusion processes is already a vast field of literature. In this introduction, I will give an entry point to this field by going over the main concepts and deriving the essential results of the area. Thus, by the end of the talk, we would have a minimal pipeline for implementing the generative model. Furthermore, I will outline several alternative ways for learning such models that the community has developed in recent years. These directions bring novel perspectives and new capabilities of generative modeling.

Zoom link:  https://pitp.zoom.us/j/98786491081?pwd=U1cvZzBQT2VUZDl5Ykd0c1lqY29aZz09

Fast Radio Bursts (FRBs) are extremely energetic, millisecond-duration radio bursts coming outside our galaxy. The burst arrival time at different frequencies implies the number of electrons it has encountered in the foreground. Therefore, FRB is considered a promising new cosmology probe. The uncertainty of the circum-burst environment is one of the biggest concerns regarding its potential as a probe. In this talk, I will review the current understanding of the FRB progenitor and the recent study of the circum-burst environment. I will also discuss the many remaining mysteries, including the seemingly diverse nature of the sources, the magneto-environment, and the 16-day periodicity I found with one source. With the current and upcoming instruments, there will be more FRBs with orders of magnitude better spatial resolution detected in the next few years. The result will be an explosion of opportunity for understanding the burst origin and probing cosmic matter distribution at various spatial scales.

Zoom link: https://pitp.zoom.us/j/92030175800?pwd=dWlGVjV0Qnh5bGhLMk1pd01yRmNKQT09

Trace map on deformation quantized algebra leads to the algebraic index theorem. We investigate a two-dimensional chiral analogue of the algebraic index theorem via the theory of chiral algebras developed by Beilinson and Drinfeld. We construct a trace map on the elliptic chiral homology of the free beta gamma-bc system using the BV quantization framework. As an example, we compute the trace evaluated on the unit constant chiral chain and obtain the formal Witten genus in the Lie algebra cohomology. This talk is based on joint work with Si Li.

Zoom link:  https://pitp.zoom.us/j/91920988875?pwd=dUE1WDI5Q21KWTUxTGNsM21nblh5Zz09