Scientific Series

The cobordism hypothesis gives a functorial bijection between oriented 

n-dimensional fully local topological field theories, valued in some 

higher category C, and the fully dualizable object of C equipped with 

the structure of SO(n)-fixed point.  In this talk I'll explain recent 

works of Haugseng, Johnson-Freyd and Scheimbauer which construct a 

Morita 4-category of braided tensor categories, and I'll report on joint 

work with Brochier and Snyder which identifies two natural subcategories 

therein which are 3- and 4-dualizable.  These are the rigid braided 

tensor categories with enough compact projectives, and the braided 

fusion categories, respectively.  I'll also explain work in progress by 

us to construct SO(3)- and SO(4)-fixed point structures in each case, 

starting from ribbon and pre-modular categories, respectively.

Applying the cobordism hypothesis, we obtain 3- and 4-dimensional fully 

local TFT's, which extend the 2-dimensional TFT's we constructed with 

Ben-Zvi and Brochier, and which conjecturally relate to a number of 

constructions in the literature, including: skein modules, quantum 

A-polynomials, Crane-Kauffmann-Yetter invariants; hence our construction 

puts these on firm foundational grounds as fully local TFT's.  A key 

feature of our construction in dimension 3 is that we require the input 

braided tensor category neither to be finite, nor semi-simple, so this 

opens up new examples -- such as non-modularized quantum groups at roots 

of unity -- which were not obtainable by earlier methods.

Port-based teleportation (PBT) is a variant of the well-known task of quantum teleportation in which Alice and Bob share multiple entangled states called "ports". While in the standard teleportation protocol using a single entangled state the receiver Bob has to apply a non-trivial correction unitary, in PBT he merely has to pick up the right quantum system at a port specified by the classical message he received from Alice. PBT has applications in instantaneous non-local computation and can be used to attack position-based quantum cryptography. Since perfect PBT protocols are impossible, there is a trade-off between error and entanglement consumption (or the number of ports), which can be analyzed using representation theory of the symmetric and unitary groups. In particular, without loss of generality the resource state can be assumed to have a “purified" Schur-Weyl duality symmetry. I will give an introduction to the task of PBT and its symmetries, and show how the asymptotics of existing formulas for the optimal performance for a given number of ports can be derived using a connection between representation theory and the Gaussian unitary ensemble.

Joint work with M. Christandl, C. Majenz, G. Smith, F. Speelman & M. Walter

In the first part of the talk, I will describe the new large N limit of tensor models, based on the “index” of graphs (in contrast to the standard large N expansion  based on the “degree”), and the associated new large D limit of matrix models. This new limit sheds an interesting light on the relation between disordered models à la SYK, tensor models and black holes. In the second part of the talk, I will apply these ideas to discuss the phase diagrams of some strongly coupled matrix quantum mechanics. The phase diagrams display many interesting features, including first and second order phase transitions and quantum critical points. Some of these phase transitions can be argued to provide a quantum mechanical description of the phenomenon of gravitational collapse. 

Detections of compact binary coalescences with Advanced LIGO and Advanced Virgo are now starting to become routine. However, thereis still considerably more information that can be gleaned from these observations, particularly as detector sensitivity and waveform modelsboth improve. We start by describing the methods currently used in LIGO/Virgo data analysis to determine the mass and spin of the remnant black hole of the binary black hole coalescences. These black holes have the most well-measured masses and spins of any stellar-mass black holes observed and comparable or better mass accuracies to Sgr A*. We also describe the method used to obtain a lower bound on the radiated energy of the binary neutron star coalescence GW170817, and discuss further information one can extract from these observations by postprocessing parameter estimation results. We also describe a method for placing constraints on properties of black hole mimickers, such as boson stars or gravastars, if binaries of these objects are to produce the signals identified as coming from binary black holes. We present initial results of the method applied to injections in simulated noise, and as a proof of principle show how it is possible to rule out or constrain the properties of a specific model of boson stars using a given detection.

Several equivalent formulations of quantum error correction condition will be introduced. Subtleties arise

when the error correction conditions hold only approximately. We will discuss an equivalent formulation that is 

robust to the approximation error. One can leverage this tool to derive the existence of approximate quantum

error correcting code at low energy subspace of CFT that reproduces aspects of the holographic quantum error

correcting code. Using the same tool, we observe that two operators with greatly differing complexity approximately

commute in an appropriate code subspace. This leads to a notion of bulk locality in the entanglement shadow,

but the precise definition of complexity seems to play an important role in determining how well these operators commute

in the subspace.

Gravitational lensing of the cosmic microwave background has emerged as a powerful cosmological probe, made possible by the development and characterization of nearly-optimal estimators for extracting the lensing signal from temperature and polarization maps. One can ask whether similar tools can be applied to upcoming "intensity maps" of emission lines at other wavelengths (e.g. 21cm). In this talk, I will present recent work in this direction, focusing in particular on the impact of gravitational nonlinearities on standard quadratic lensing estimators. I will show how these nonlinearities can provide a significant contaminant to lensing reconstruction, even for observations at reionization-era redshifts, but will also describe how this contamination can largely be mitigated by modifying the lensing estimator. Finally, I will present estimates for the detectability of lensing in ongoing and future intensity mapping surveys.

String theory provides us with 8d supersymmetric gauge theories with gauge algebras su(N), so(2N), sp(N), e_6, e_7 and e_8, but no construction for so(2N+1), f_4 and g_2 is known. If string theory is universal in 8 dimensions, this pattern requires explanation. I will show that the theories for f_4 and so(2N+1) have a global gauge anomaly in flat space, while g_2 does not have it. Surprisingly, we also find that the sp(N) theories, arising from example from O7^+ planes in string theory, have a subtler gauge anomaly. This subtler anomaly, in contrast to the one in flat space, could in principle be canceled by a topological analogue of the Green-Schwarz mechanism. I will discuss one simple example of such a generalized anomaly cancellation mechanism in three dimensions, and then explain why the generalized Green-Schwarz term required in 8 dimensions to make the O7^+ consistent is necessarily a more subtle generalization of a Chern-Simons coupling

Microwave Kinetic Inductance Detectors, or MKIDs, are superconducting detector arrays that can measure the energy and arrival time of individual optical through near-IR photons without read noise or dark counts.  I will discuss our recent work and results from the first two MKID Integral Field Spectrographs (IFSs) for high contrast imaging, DARKNESS/SDC at the Palomar 200" and MEC/SCExAO on Subaru. I will then look at the future of MKIDs and their potential on 30-m class telescopes like the TMT, and explore a fascinating new application in the detection of light scalar dark matter. 

In this talk I will describe joint work in progress with Andre Henriques to construct examples of Graeme Segal's functorial definition of 2d chiral conformal field theory. While Segal's definition originated in the 1980's, constructive aspects of the theory continue to be challenging, especially with regard to higher genus surfaces. I will motivate and introduce Segal's definition, and describe a new approach to constructing examples using von Neumann algebras. 

I show that dark matter abundance can be set by the decoupling of inelastic scatterings instead of annihilations. Coscattering points to dark matter that is exponentially lighter than the weak scale and has a suppressed annihilation rate, avoiding constraints from indirect detection. The late decays of the states into which dark matter upscatters, can lead to observable distortions to the blackbody spectrum of the cosmic microwave background. 

In this talk, I will summarize the status of the numerical evaluation of spin foam amplitudes focusing on the Lorentzian EPRL-FK model. I will illustrate how numerical methods can lift some limitations of the theory helping us understand better its continuum and semi-classical limit.