Scientific Series

One can associate to any finite graph Q the skew-symmetic Kac-Moody Lie algebra g_Q. While this algebra is always infinite, unless Q is a Dynkin diagram of type ADE, g_Q shares a lot of the nice features of a semisimple Lie algebra. In particular, the cohomology of Nakajima quiver varieties associated to Q gives a geometric representations of g_Q. Encouraged by this story, one could hope to define the Yangian of g_Q, for general Q, as a subalgebra of the algebra of endomorphisms of cohomology of quiver varieties. In fact there are two approaches to doing this: firstly via the stable envelope construction of Maulik and Okounkov, secondly via the preprojective Hall algebra of Schiffmann and Vasserot. Via another Hall algebra construction, due to Kontsevich and Soibelman, and work of myself and Meinhardt on BPS Lie algebras, these approaches turn out to be more or less the same. In showing this we show that the correct Lie algebra of endomorphisms associated to Q is cohomologically graded, with zeroeth piece the old Kac-Moody Lie algebra - the best way to build a (Borcherds) Lie algebra out of Q is directly from geometric representation theory.

I discuss the canonical degrees of freedom of metric Einstein gravity on a null surface. The constraints are interpreted as conservation equations of a boundary current. Gravitational fluxes are identified, and the Hamiltonians of diffeomorphism symmetry are discussed. Special attention is given to the role of a modification of the phase space at the boundary of the null surface. Based on 1802.06135 with Laurent Freidel.

Despite considerable effort, magic state distillation remains one of the leading candidates to achieve universal fault-tolerant quantum computation. However, when analyzing magic state distillation schemes, it is often assumed that gates belonging to the Clifford group can be implemented perfectly. In many current quantum technologies, two-qubit Cliffords gates are amongst the noisiest components of quantum computers. In this talk I will present a new scheme for preparing magic states with very low overhead that uses flag qubits. I will then compare our scheme to leading magic state distillation methods and show that the overhead can be reduced by orders of magnitude.

The two-point functions <O^n(x) Obar^n(y)> for generator O of Coulomb branch chiral rings in D=4 N=2 SCFT will be determined universally to all orders in 1/n by the theory's a-anomaly.
The calculation will be done using the method of large-charge expansion presented in [1706.05743]; the absence of F-terms in the (R-charge)^(-1) expansion of the effective action ensures this universality.
I will also comment on the non-universal and non-perturbative corrections to the two-point functions whose leading piece was numerically shown to go as O(exp(-sqrt(n))).  

While the term “wide-field telescope” might sound like an oxymoron, a strong argument can be made that wide-field instruments lie behind much of the success of Canadian astronomy. Furthermore, despite the large size of the optical-IR community in Canada, this success has been made possible by considering multiple wavelength windows, from gamma to radio, and access to a suite of facilities. Over the past two decades, through a pair of 10-year Long Range Plans, Canadian astronomy has carefully structured its facility access, to ensure, as best as can be reasonably hoped, that the community maintains access to world-leading facilities. I’ll summarize the progression of the community vision on wide-field astronomy, highlighting successes and some missteps. As we head towards the creation of the 3rd Canadian Long Range Plan for astronomy, I’ll also present some personal views on what scientific leadership means and the challenges that it presents for a smaller country (at least in the G7 sense!) like Canada.

Three dimensional fracton phases are new type of phases featuring exotic excitations called fractons. They are gapped point-like excitations constrained to move in sub-dimensional space. In this talk, I will present the gapped fracton topological order discovered in exact solvable models and gapless fracton phase described by U(1) symmetric tensor gauge theories. Their relation with ordinary topological ordered phase would be discussed in detail. Particularly, the fracton topological order exhibited in an exact solvable model called X-cube model can be constructed by coupling toric code layers. And it can also be obtained from a particular rank-2 symmetric tensor gauge theory called scalar charge theory by Higgs mechanism and partial confinement transition.

After the detection of black hole and neutron star binary mergers at LIGO/Virgo, gravitational wave becomes a new observational channel that we didn't have access to years ago.

It is an interesting question to ask what kind of new particle physics this channel can probe.

To answer this question, one needs to fill the gap between the scales of the astrophysical processes and the fundamental structures.

In this talk, I will demonstrate a few ways of extracting particle physics information directly from binary merger events of neutron stars and boson stars, and using this information to constrain well motivated dark sectors, including dark gauge boson and axion like particles.

An outline of future directions will also be discussed.

Line Intensity Mapping has emerged as a powerful tool to probe the large-scale structure across redshift, with the potential to shed light on dark energy at low redshift and the cosmic dawn and reionization process at high redshift.  Multiple spectral lines, including the redshifted 21cm, CO, [CII], H-alpha, and Lyman-alpha emissions, are promising tracers in the intensity mapping regime, with several experiments on-going or in the planning.  I will discuss results from current pilot programs, prospects for the upcoming TIME experiment, and the outlook of future space missions such as SPHEREx.  I will illustrate how the use of cross-correlation between multiple line intensity maps will enable unique and insightful measurements, revealing for example the tomography of reionization and the physics of multiple phases of the interstellar medium across redshift.

Recent progress in determining scattering phase shifts, and hence, resonance properties from lattice QCD in finite volumes is presented.

The relationship between finite-volume stationary-state energies and the two-particle scattering K-matrix is discussed.

Details of the Monte Carlo computations of the finite-volume two-particle energies are described.

Results for pion-pion, kaon-pion, and nucleon-pion scattering are presented.

The large j asymptotic behavior of 4-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large j asymptotic behavior is determined by critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are phases asymptotically, whose exponents equal to Regge action of gravity. The amplitude also contains critical configurations corresponding to non-degenerate split signature 4-simplices and degenerate vector geometries.  

Searching for a proper set of order parameters which distinguishes different phases of matter sits in the heart of condensed matter physics. In this talk, I discuss topological invariants as (non-local) order parameters for symmetry protected topological (SPT) phases of fermions in the presence of time-reversal symmetry. It turns out that topological invariants provide a natural definition for the partial transpose of density matrices. The partial transpose can then be used to define an entanglement measure (analog of entanglement negativity) for mixed states of fermions. I will show that this quantity captures the mixed state entanglement in fermionic SPTs as well as in a system of free fermions with a Fermi surface.