Scientific Series

In 2012, Maulik proved a conjecture of Oblomkov-Shende relating: (1) the Hilbert schemes of a plane curve (alternatively, its compactified Jacobian), (2) the HOMFLY polynomials of the links of its singularities. We recast his theorem from the viewpoint of representation theory. For a split semisimple group G with Weyl group W, we state a stronger conjecture relating two virtual modules over Lusztig's graded affine Hecke algebra,  constructed from: (1) fibers of a parabolic Hitchin map, (2) generalized Bott-Samelson spaces attached to conjugacy classes in the braid group of W. In arbitrary type, we can establish an infinite family of cases where it holds. Time permitting, we'll indicate how the new conjecture relates to P = W phenomena in nonabelian Hodge theory.

The n-point correlation functions (n>2) of primordial fluctuations, known as primordial non-Gaussianities, encode rich information about the physical degrees of freedom and their interactions at inflation scale, and can be viewed as signals from a cosmological collider with huge energy. In this talk we introduce recent theoretical attempts to extract new physics at the inflation scale from primordial non-Gaussianities, including possible discovery channels, the background signals from the standard model, and signals from new physics such as heavy neutrinos, and a possible way to turn inflation into a Higgs collider.

The history of the baryonic (normal) matter in the universe is an excellent probe of the  formation of cosmic structures and the evolution of galaxies.  Over the last decade, considerable effort has gone into investigating the physics of baryonic material, particularly after the epoch of Cosmic Dawn: signalling the birth of the earliest stars and 
galaxies --- widely considered the ‘final frontier’ of observational cosmology today. The technique of (line) ‘intensity mapping’ (IM) has emerged as a powerful tool to explore this phase of the universe by measuring the integrated emission from sources over a broad range of frequencies. I will overview my current research on the mapping of atomic hydrogen over 12  billion years of cosmic time, based on a data-driven framework developed for interpreting current and future IM observations. I will then describe extensions of this approach which provide a comprehensive picture of molecular gas evolution, and interpret results from ongoing observations. This opens up the exciting potential of constraining fundamental physics from Cosmic Dawn.

Tensor models exhibit a melonic large $N$ limit: this is a non trivial family of Feynman graphs that can be explicitly summed in many situations. In $d$ dimensions, they give rise to a new family of conformal field theories and provide interesting examples of the renormalization group flow from a free theory in the UV to a melonic large $N$ CFT in the IR. 

We consider here a bosonic tensor model in rank three and $d<4$ dimensions. After giving a short introduction to tensor models, I will present the renormalization group flow of the model. At leading order in $1/N$ but non perturbatively in the coupling constants, we found a real and infrared fixed point.

Ground-based gravitational wave observatories have begun to uncover a large number of compact binary coalescences in the universe through gravitational wave signals. I will discuss novel and effective techniques we have developed recently to analyze the publicly available LIGO/Virgo bulk strain data from scratch. Built on simple ideas and easy to implement, those address the questions of template bank construction, signal processing, trigger ranking, and fast parameter estimation. Applying those techniques, we searched for compact binary mergers during the LIGO/Virgo O1 and O2 runs, and detected a few binary black hole mergers in addition to what have been reported in the literature.

We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such codes generalize stabilizer QLDPC codes, which are exact quantum error-correcting codes with sparse, low-weight stabilizer generators (i.e. each stabilizer generator acts on a few qubits, and each qubit participates in a few stabilizer generators). Our investigation is motivated by an important question in Hamiltonian complexity and quantum coding theory: do stabilizer QLDPC codes with constant rate, linear distance, and constant-weight stabilizers exist? We show that obtaining such optimal scaling of parameters (modulo polylogarithmic corrections) is possible if we go beyond stabilizer codes: we prove the existence of a family of [[N,k,d,ε]] approximate QLDPC codes that encode k = Ω(N/polylog N) into N physical qubits with distance d = Ω(N/polylog N) and approximation infidelity ε = 1/polylog N. We prove the existence of an efficient encoding map, and we show that arbitrary Pauli errors can be locally detected by circuits of polylogarithmic depth. Finally, we show that the spectral gap of the code Hamiltonian is Ω(N^(-3.09)) (up to polylog(N) factors) by analyzing a spacetime circuit-to-Hamiltonian construction for a bitonic sorting network architecture that is spatially local in polylog(N) spatial dimensions. (Joint work with Elizabeth Crosson, Chinmay Nirkhe, and Henry Yuen, arXiv:1811.00277)

Einstein is well known for his rejection of quantum mechanics in the form it emerged from the work of Heisenberg, Born and Schrodinger in 1926. Much less appreciated are the many seminal contributions he made to quantum theory prior to his final scientific verdict: that the theory was at best incomplete. In this talk I present an overview of Einstein’s many conceptual breakthroughs and place them in historical context. I argue that Einstein, much more than Planck, introduced the concept of quantization of energy in atomic mechanics. Einstein proposed the photon, the first force-carrying particle discovered for a fundamental interaction, and put forward the notion of wave-particle duality, based on sound statistical arguments 14 years before De Broglie’s work. He was the first to recognize the intrinsic randomness in atomic processes, and introduced the notion of transition probabilities, embodied in the A and B coefficients for atomic emission and absorption. He also preceded Born in suggesting the interpretation of wave fields as probability densities for particles, photons, in the case of the electromagnetic field. Finally, stimulated by Bose, he introduced the notion of indistinguishable particles in the quantum sense and derived the condensed phase of bosons, which is one of the fundamental states of matter at low temperatures. His work on quantum statistics in turn directly stimulated Schrodinger towards his discovery of the wave equation of quantum mechanics. It was only due to his rejection of the final theory that he is not generally recognized as the most central figure in this historic achievement of human civilization.   

Recently, a new family of correlated honeycomb materials with strong spin-orbit coupling have been promising candidates to realize the Kitaev spin liquid. In particular, a half-integer quantized thermal Hall conductivity was reported in alpha-RuCl3 under the magnetic field. Using a generic nearest neighbour spin model with bond-dependent interactions, I will present numerical evidence of an extended regime of quantum spin liquids. I will also discuss how to achieve a chiral spin liquid near ferromagnetic Kitaev interaction in the presence of the magnetic field leading to the quantized thermal Hall conductivity.

We derive Born’s rule and the density-operator formalism for quantum systems with Hilbert spaces of finite dimension. Our extension of Gleason’s theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

This talk is about a new type of string theory with a non-relativistic conformal field theory on the world-sheet, as well as a non-relativistic target space geometry. Starting with the relativistic Polyakov action with a fixed momentum along a non-compact null-isometry, we can take a scaling limit that gives the non-relativistic string, including an interesting intermediate step. This can in particular be applied to a string on AdS5 x S5. In this case the scaling limit realizes a limit of AdS/CFT that on the field theory side gives a quantum mechanical theory known as Spin Matrix theory. We review that Spin Matrix theory is a finite-N version of nearest neighbor spin chains, from which one can find a long-wavelength semi-classical description using sigma-model such as the Landau-Lifshitz sigma-model. Hence, we can show that both sides of the AdS/CFT gives, in this limit, equivalent non-relativistic sigma-models that we are able to write down in a fully covariant manner, and show that it has a non-relativistic local symmetry that realizes the Galilean Conformal Algebra (GCA). This suggests that one has a holographic duality between the quantum mechanical theory of Spin Matrix theory, and the non-relativistic string. This could provide a more tractable holographic duality in which one can study the emergence of non-relativistic strings, geometry and gravity.

We present the complete history of structure formation in a simple dissipative dark-sector model. The model has only two particles: a dark electron and a dark photon. Dark-electron perturbations grow from primordial overdensities, become non-linear, and form dense, dark galaxies. We show that asymmetric dark stars and black holes form within the Milky Way from the collapse of dark electrons. These exotic compact objects may be detected and their properties measured at new high-precision astronomical observatories, giving insight into the particle nature of the dark sector without the requirement of non-gravitational interactions with the visible sector.

Fundamental physics traditionally views the dynamical laws governing the world as time reversal invariant. The evident arrow of time of nature is then held to be an accident, emerging as we coarse grain and originating in the improbable choice of initial conditions. The main pillar which supports this time-symmetric lifestyle is the fluctuation-dissipation theorem, which connects purely time-symmetric microscopic equations to the emergence of a macroscopic arrow of thermodynamics. I will describe arguments from statistical physics claiming that existing proofs of this theorem are faulty and do not demonstrate the emergence of an arrow from time-symmetric laws. I will argue that, as a result of this assumption of time symmetry, we cosmologists stand to pay an unreasonable price concerning what we’re expected to explain. I argue for instead to turn this picture around and propose a fundamental theory of cosmology and quantum gravity which is fundamentally time asymmetric and based on time-irreversible laws. I will describe a new class of models of quantum space-time, energetic causal sets, in which space-time itself, as well as aspects of quantum theory, emerge under natural conditions. The framework is based on arXiv:1307.6167 and subsequent papers in collaboration with Lee Smolin.