Scientific Series

We study the effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals and Maurer-Cartan equations for chiral vertex operators. The generating functions are proven to be quasi-modular forms. As an application, we construct an exact solution of quantum B-model (BCOV theory) in complex one dimension that solves the higher genus mirror symmetry conjecture on elliptic curves. The talk is based on arXiv: 1612.01292[math.QA]

Anomalies are a ubiquitous phenomenon in quantum mechanics whereby a classical
symmetry is irrevocably violated by quantization. Anomalies not only constrain the
space of classical theories than are consistent with quantum mechanics but are
responsible for rich, surprising and experimentally tested physical phenomena.
In this talk I will give a non-technical, bird's eye introduction to anomalies.

CHIME is a new interferometric telescope at radio frequencies 400-800 MHz.  The mapping speed (or total statistical power) of CHIME is among the largest of any radio telescope in the world, and the technology powering CHIME could be used to build telescopes which are orders of magnitude more powerful.  This breakthrough sensitivity has the power to revolutionize radio astronomy, but meeting the computational challenges will require breakthroughs on the algorithmic side.  I'll give a status update on CHIME, with an emphasis on new algorithms being developed to search for fast radio bursts and pulsars.

We will describe a formulation of the Batalin-Vilkovisky formalism using derived symplectic geometry.  In this setting, the classical master equation of the BV formalism describes a space of coisotropic structures.  Using this approach, we resolve a conjecture of Felder-Kazhdan regarding BRST cohomology.  Time permitting, we will also describe applications of these ideas to more general quantization problems.

Since its first discovery in 1986, high-Tc superconductors have been attracting constant interests and meticulous efforts from both theorists and experimentalists, not merely due to its large transition temperature, but also because it offers a well characterized laboratory for the study of exotic phenomena such as quantum criticality, non-Fermi liquid behavior, and intertwined orders. One pressing question in the field is the role played by disorder:

inevitable in real materials, disorder is able to fundamentally alter the properties of the system under certain circumstances. In this talk, we will discuss from a theoretical point of view, how different types of disorders affect various electronic orders in copper-based high-Tc superconductors. We also discuss the implications in experiments, and investigate the possibility of generalizing our conclusions to a variety of other physical systems.

A research line that has been very active recently in quantum information is that of recoverability theorems. These, roughly speaking, quantify how well can quantum information be restored after some general CPTP map, through particular 'recovery maps'. In this talk, I will outline what this line of work can teach us about quantum thermodynamics.

On one hand, dynamical semigroups describing thermalization, namely Davies maps, have the curious property of being their own recovery map, as a consequence of a condition named quantum detailed balance. For these maps, we derive a tight bound relating the entropy production at time t with the state of the system at time 2t, which puts a strong constraint on how systems reach thermal equilibrium. 
On the other hand, we also show how the Petz recovery map appears in the derivation of quantum fluctuation theorems, as the reversed work-extraction process. From this fact alone, we show how a number of useful expressions follow. These include a generalization of the majorization conditions that includes fluctuating work, Crooks and Jarzynski's theorems, and an integral fluctuation theorem that can be thought of as the second law as an equality.

Measurements of the cosmic microwave background (CMB) have proven to be a powerful probe of the physics of our universe. CMB observations are helping to address fundamental questions, such as the nature of dark energy and dark matter, and are being used to probe the physics of inflation at energies a trillion times higher than the Large Hadron Collider. Recent measurements led to several exciting first detections, including CMB lensing, massive galaxy clusters, the large-scale velocity field, and the “B-mode” component of the polarization field. These results have been enabled by the development of superconducting detectors and optics instrumentation, but we are now approaching the limits of current telescope facilities. Continuing advances in CMB research require greater sensitivity through major gains in optical throughput.

The CCAT-prime extreme field-of-view submillimeter telescope on Cerro Chajnantor will meet this challenge. The six-meter aperture telescope is designed to observe between 350um - 3mm and is capable of mapping the CMB roughly 10x faster than current observatories, making it a potential platform for the next generation “Stage IV” CMB survey. The first light instrument will take advantage of the unique CCAT-prime capabilities and site to characterize the large-scale velocity field and CMB polarization. In addition, CCAT-prime will enable spectroscopic intensity mapping of [CII] from early stars and galaxies during reionization and low-redshift galactic ecology. The intensity mapping measurements can be cross-correlated with upcoming neutral hydrogen surveys, and this combination may eventually characterize primordial non-Gaussianities beyond the reach of CMB measurements to provide new insights into the high-energy physics of inflation.

This talk applies effective field theory to the back-reaction of sources with finite size but infinite mass. The main tool for calculating back-reaction is a general relation between a source's effective action and the boundary conditions of `bulk’ fields in the near-source limit. As applied to the Maxwell (or Einstein) fields for point sources this boundary condition reproduces standard Gauss’ Law expressions, but the same arguments imply source-dependent boundary conditions for the Schrodinger (or Dirac) field of an orbiting particle. As applied to the quantum mechanics of a particle interacting with a source through an inverse-square potential EFTs remove the guess-work from the (well-known) ambiguities in the determination of boundary conditions at the origin, and provides a simple interpretation of the classical renormalization effects that are known to arise in this case. EFT arguments show why the RG evolution associated with this classical renormalization is likely universal for a great many types of point sources. The EFT boundary conditions also modify how finite-size effects alter bound-state orbits in the Coulomb problem, and in particular give them a non-standard dependence on the mass of the orbiting particle. It is argued that this might provide a solution to the `proton-radius puzzle’, in which experiments seem to indicate a different proton radius depending on whether or not it is measured using electrons or muons.

Motivated by the question about reconstructing a Conformal field theory from the data of a subfactor of finite index, Jones studied the continuous limit of the periodic quantum spin chain which Thompson group acts on. Based on planar algebras, the topological axiomatization of subfactors, we will illustrate the idea of the correspondence between the skein theory of planar algebras and presentation of Thompson groups.

The affine Grassmannian is the analog of the Grassmannian for the loop group. They are very important objects in mathematical physics and the Geometric Langlands program. In this talk, I will explain my recent work on the central degeneration of semi-infinite orbits, Iwahori orbits and Mirkovic-Vilonen cycles in the affine Grassmannian. I will also use lots of convex polytopes to illustrate my results. In addition, I will explain the connections between my work and other parts of geometric representation theory and combinatorial algebraic geometry.  

Bosonic symmetric protected topological (BSPT) phases are bosonic anagolue of electron topological insulators and superconductors. Despite the theoretical progresses of classifying these states, little attention has been paid to experimental realization of BSPT states in dimensions higher than 1. We propose bilayer graphene system in a out-of-plane magnetic field with Coulomb interaction is a natural platform for BSPT states with $U(1)\times U(1)$ symmetry. We also propose that the quantum phase transition between the BSPT state and the trivial state, which may be tuned by an out-of-plane electric field, could be a novel transition with only gapless bosonic degrees of freedom. In the second part of the talk we will discuss the out-of-time-order correlation (OTOC) and its application in many-body localized and marginal MBL systems. We demonstrate, in marginal MBL systems, the scrambling time follows a stretched exponential scaling with the distance between the operators, which demonstrates Sinai diffusion of quantum information and the enhanced scrambling by the quantum criticality in non-chaotic systems.