Talks

Information theory offers mathematically precise theory of communication and data storage that guided and fueled the information age.  Initially, quantum effects were thought to be an annoying source of noise, but we have since learned that they offer new capabilities and vast opportunities. Quantum information theory seeks to identify, quantify, and ultimately harness these capabilities. A basic resource in this context is a noisy quantum communication channel, and a central goal is to figure out its capacities---what can you do with it?  I’ll highlight the new and fundamentally quantum aspects that arise here, such as the role of entanglement, ways to quantify it, and bizarre new kinds of synergies between resources.  These ideas elucidate the nature of communication in a quantum context, as well as revealing new facets of quantum theory itself.

Have you always wanted to know: What the symmetries of nature are? How black holes process quantum information? What the ultimate UV description of our universe is? Then join me as I continue to develop a new framework to describe scattering:  Celestial Holography.

The Celestial Holography framework applies the holographic principle to spacetimes with vanishing cosmological constant by mapping 4D S-matrix elements to correlators in a 2D conformal field theory. This map possesses a number of surprising features. For example, it emphasizes infinite dimensional symmetry enhancements, which are typically hidden in IR factorization theorems for amplitudes; reorganizes collinear limits as CFT operator product expansions; and mixes UV and IR behavior in a manner that may allow us to make general claims about scattering not obvious from perturbation theory.

Can we show that the UV behavior of amplitudes must be stringy? Can we bootstrap celestial CFTs? Can we unify tools from Loop Quantum Gravity and String Theory?

Maybe, with your help!

I will discuss the conditions satisfied by the 2 → 2 scattering amplitude in unitarity and causal theories, presenting a simple formulation in term of moments of a positive measure. I will identify complete subsets of two-sided constraints, suitable to bound Effective Field Theories (EFTs) at any finite order in the energy expansion. I will also discuss  the importance of IR loop effects on these bounds. A consequence of this study is that EFTs in which the scattering amplitude in some regime grows in energy faster than E6 (e.g. higher spin particles with masses smaller than their inverse size) cannot be UV-completed.

Modeling galaxy-dark matter connection is essential in deriving unbiased cosmological constraints from galaxy clustering observations. We show that a more physically motivated galaxy-dark matter incorporating secondary (assembly) biases results in more accurate predictions of galaxy clustering, yields novel insights into effects such as baryonic feedback, and significantly reduces the tension in galaxy lensing. We further present progress and opportunities in building a multi-tracer galaxy-dark matter connection framework that is rich in features and highly efficient, enabling more robust cosmological analyses with upcoming DESI data.

Stellar streams are a powerful tool for mapping of the Galactic matter distribution. Thanks to Gaia we now have full 6D (complete phase-space) view of a quickly growing subset of the Milky Way streams. These stars are precious as they can shed light not only on the broad-brush structure of the Galaxy, but also reveal small time-evolving perturbations of the Galactic potential. I will use the Sagittarius and the Orphan streams to present the most recent measurements of the dark matter halo of the Milky Way and one of its sub-halos.

When the twist angle of a bilayer graphene is near the ``magic'' value, there are four narrow bands near the neutrality point, each two-fold spin degenerate. These bands are separated from the rest of the bands by energy gaps. In the first part of the talk, the topology of the narrow bands will be discussed, as well as the associated obstructions --or lack there of -- to construction of a complete localized basis [1,3].

In the second part of the talk, I will present a two stage renormalization group treatment [4] which connects the continuum Hamiltonian at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only, which is valid at distances much longer than the moire period. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian will be determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step.

In the last part of the talk, the states favored by electron-electron Coulomb interactions within the narrow bands will be discussed. Analytical and DMRG results based on 2D localized Wannier states [2,5], 1D localized hybrid Wannier states [3] and Bloch states [3,4] will be compared. Topological and symmetry constraints on the spectra of charged and neutral excitation[4] for various ground states, as well as non-Abelian braiding of Dirac nodes[3] , will also be presented.

[1] Jian Kang and Oskar Vafek, Phys. Rev. X 8, 031088 (2018).

[2] Jian Kang and Oskar Vafek, Phys. Rev. Lett. 122, 246401 (2019)

[3] Jian Kang and Oskar Vafek, Phys. Rev. B 102, 035161 (2020)

[4] Oskar Vafek and Jian Kang Phys. Rev. Lett. 125, 257602 (2020)

[5] Bin-Bin Chen, Yuan Da Liao, Ziyu Chen, Oskar Vafek, Jian Kang, Wei Li, Zi Yang Meng arXiv:2011.07602

We will describe an approach to the theory of fundamental particlesbased on finite-dimensional quantum algebras of observables. We will explain why the unimodularity of the color group suggests an interpretation of the quarklepton symmetry which involves the octonions and leads to the quantum spaces underlying the Jordan algebras of octonionic hermitian 2 × 2 and 3 × 3 matrices as internal geometry for fundamental particles. In the course of this talk, we will remind shortly why the finite-dimensional algebras of observables are the finite-dimensional euclidean Jordan agebras and we will describe their classifications. We will also explain our differential calculus on Jordan algebras and the theory of connections on Jordan modules. It is pointed out that the above theory of connections implies potentially a lot of scalar particles.