Scientific Series

This seminar will be a continued discussion on the topic of last week's seminar: 

I will describe some general mathematical structures expected to arise from field theories with boundary conditions in terms of factorization algebras, and outline some results and future directions in the study of boundary chiral algebras for 3d N=4 theories following the work of Costello and Gaiotto.

Given by Dylan Butson.

Black hole entropy is a robust prediction of quantum gravity with no observational test to date. We use the Bekenstein-Hawking entropy formula to determine the probability distribution of the spin of black holes at equilibrium in the microcanonical ensemble. We argue that this ensemble is relevant for black holes formed in the early universe and predicts the existence of a population of black holes with zero spin. Observations of such a population at LIGO, Virgo, and future gravitational wave observatories would provide the first experimental test of the statistical nature of black hole entropy.

The source of about half of the heaviest elements in the Universe has been a mystery for a long time. Although the general picture of element formation is well understood, many questions about the nuclear physics processes and particularly the astrophysical details remain to be answered. Here I focus on recent advances in our understanding of the origin of the heaviest and rarest elements in the Universe.

The precise relationship between post-selected classical and 
post-selected quantum computation is an open problem in complexity 
theory. Post-selection has proven to be a useful tool in uncovering some 
of the differences between quantum and classical theories, in 
foundations and elsewhere. This is no less true in the area of 
computational complexity -- quantum computations augmented with 
post-selection are thought to be vastly more powerful than their 
classical counterparts. However, the precise reasons why this might be 
the case are not well understood, and no rigorous separations between 
the two have been found. In this talk, I will consider the difference in 
computational power of classical and quantum post-selection in the 
computational query complexity setting.

We define post-selected classical query algorithms, and relate them to 
rational approximations of Boolean functions; in particular, by showing 
that the post-selected classical query complexity of a Boolean function 
is equal to the minimal degree of a rational function with nonnegative 
coefficients that approximates it (up to a factor of two). For 
post-selected quantum query algorithms, a similar relationship was shown 
by Mahadev and de Wolf, where the rational approximations are allowed to 
have negative coefficients. Using our characterisation, we find an 
exponentially large separation between post-selected classical query 
complexity and post-selected quantum query complexity, by proving a 
lower bound on the degree of rational approximations to the Majority 
function.

One long standing question on quantum non-locality is the quest for an informational principle explaining quantum correlations. Many candidates for such a principle have been proposed with partial success, but none fully explaining quantum correlation. Most of these principles rely on the analysis of the multipartite conditional probabilities. In this talk I will briefly review a few results we had when, instead of analysing multipartite probabilities, we analysed sequences of results from non-local boxes. First, that non-local deterministic boxes cannot be computable. Second, that pseudorandom inputs allow for a local model explaining non-local correlations. Finally, I will present a simple principle that rules out many non-physical sequences of experiments, and a unified view of local and non-signalling correlations based on sequences.

I will describe some general mathematical structures expected to arise from field theories with boundary conditions in terms of factorization algebras, and outline some results and future directions in the study of boundary chiral algebras for 3d N=4 theories following the work of Costello and Gaiotto.

In crystals, quantum electrons can be spatially distributed in a way that the bulk solid supports macroscopic electric multipole moments, which are deeply 

related with emergence of topology insulators in condensed matter systems. However, unlike the classical electric multipoles in open space, 

defining electric multipoles in crystals is a non-trivial task. So far, only the dipolar moment, namely polarization, has been successfully defined and served as a classic example of topological insulators. 

In this talk, we propose the general definition, i.e., many-body invariants, for electric multipoles in crystals, which are related with recently-discovererd higher-order topological insulators. 

Our invariants are designed to measure the distribution of electron charge in unit cells and thus can detect multipole moments purely from the bulk ground state wavefunctions. 

We provide analytic as well as numerical proofs for our invariants. Application of our invariants to spin systems as well as various other aspects of the many-body invariants will be briefly discussed.

I argue that we do not understand gauge theory as well as we think when boundaries are present. I will briefly explain the conceptual and technical issues that arise at the boundary.  I will then propose a tentative resolution, which requires us to think of theories not in spacetime, but in field-space. 

There is observational evidence that the X-ray continuum source that creates the broad fluorescent emission lines in some Seyfert Galaxies may be compact and located at a few gravitational radii above the black hole. We consider two scenarios for the X-ray emission. The first possibility is that the X-rays may be produced by particles accelerated in an electrostatic gap at the base of a putative jet. However, our detailed study of the gap kinetic physics and scaling suggests that the energetics is not enough in these environments. The second possibility is that the compact X-ray emitting source may be powered by small scale flux tubes near the black hole that are attached to the orbiting accretion disk. Our force-free simulations show that the field linking the black hole and the disk can get twisted up by the differential rotation to form a magnetic tower. When the confinement provided by the field from the outer disk is strong, the built-up magnetic tower can quickly become kink unstable, which leads to continuous reconnection and dissipates most of the energy extracted from the rotating black hole. This could in principle power a hot X-ray emitting region above the black hole.

Bernstein operators are vertex operators that create and annihilate Schur polynomials. These operators play a significant role in the mathematical formulation of the Boson-Fermion correspondence due to Kac and Frenkel. The role of this correspondence in mathematical physics has been widely studied as it bridges the actions of the infinite Heisenberg and Clifford algebras on Fock space. Cautis and Sussan conjectured a categorification of this correspondence within the framework of Khovanov's Heisenberg category. I will discuss how to categorify the Bernstein operators and settle the Cautis-Sussan conjecture, thus proving a categorical Boson-Fermion correspondence.

The elliptic quantum (toroidal) group U_{q,p}(g) is an elliptic and dynamical analogue of the Drinfeld realization 
of the affine quantum (toroidal) group U_q(g). I will discuss an interesting connection of its representations with 
a geometry such as an identification of the elliptic weight functions derived by using  the vertex operators with 
the elliptic stable envelopes in [Aganagic-  Okounkov ’16] and correspondence between the Gelfand-Tsetlin bases 
of a finite dimensional representation of U_{q,p} with the fixed point classes in the equivariant elliptic cohomology.

Cosmic Microwave Background (CMB) is a powerful probe to the Universe which carries signatures of cosmic secrets over a vast range of redshifts. Along with spatial fluctuations, spectral distortions of CMB blackbody are also a rich source of cosmological information. In my talk, I will introduce a new kind of spectral distortion of CMB which can arise due to the conversion of CMB photons into Axion-Like Particles (ALPs) in the presence of an external magnetic field. This effect leads to both polarized and unpolarized spatially varying spectral distortion signal with a unique spectral shape when CMB photons undergo resonant and non-resonant conversion into ALPs in the presence of the magnetic field of Milky Way, galaxy clusters and voids. I will discuss the spatial structure of this distortion which can arise from Milky Way and galaxy clusters and will show its uniqueness from other known cosmological and astrophysical signals. I will present the first all-sky map of this distortion which is obtained using the data of Planck satellite and will discuss the capability of this new cosmological window to probe ALPs from the upcoming ground-based and space-based CMB experiments such as CMB-S4, LiteBIRD, Simons Observatory, etc.