Scientific Series

A recent construction of HOMFLY-PT knot homology by Oblomkov-Rozansky has its physical origin in “B-twisted” 3D N=4 gauge theory, with adjoint and fundamental matter. Mathematically, the construction uses certain categories of matrix factorization. We apply 3D Mirror Symmetry to identify an A-twisted mirror of this construction. In the case of algebraic knots, we find that knot homology on the A side gets expressed as cohomology of affine Springer fibers (related but not identical to work if Gorsky-Oblomkov-Rasmussen-Shende). More generally, we propose a Fukaya-Seidel category mirror to the Oblomkov-Rozansky matrix factorization. Joint work with N Garner, J Hilburn, A Oblomkov, and L Rozansky.

Black holes in the background of the AdS soliton are, according to the gauge/gravity correspondence, dual to droplets of deconfined plasma surrounded by a confining vacuum. In this talk I will present, for the first time, the real time dynamics of finite energy black holes in these backgrounds. We consider horizonless initial data sourced by a massless scalar field. Upon time evolution, prompt scalar field collapse produces an excited black hole that eventually settles down to equilibrium at the bottom of the AdS soliton. Radiation in these backgrounds is carried by a set of massive states that, in the dual field theory, can be interpreted as particles. Thus, our results are relevant to describe the out-of-equilibrium dynamics in strongly coupled gauge theories that exhibit confinement. This is work in progress in collaboration with Hans Bantilan and David Mateos.

 Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. HQECC give a mapping of states and observables. However, they do not map local bulk Hamiltonians to local Hamiltonians on the boundary. In this work, we combine HQECC with Hamiltonian simulation theory to construct a bulk-boundary mapping between local Hamiltonians, whilst retaining all the features of the HQECC duality. This allows us to construct a duality between models, encompassing the relationship between bulk and boundary energy scales and time dynamics.

It also allows us to construct a map in the reverse direction: from local boundary Hamiltonians to the corresponding local Hamiltonian in the bulk. Under this boundary-to- bulk mapping, the bulk geometry emerges as an approximate, low-energy, effective theory living in the code-space of an (approximate) HQECC on the boundary. At higher energy scales, this emergent bulk geometry is modified in a way that matches the toy models of black holes proposed previously for HQECC. Moreover, the duality on the level of dynamics shows how these toy-model black holes can form dynamically.

We will talk about recent progress in NMR technologies simulating topological phases. We will describe how states are prepared, how they are evolved in time and various tricks that we can play with it, including measurements of topological properties such as modular matrices, and thus potentially applied for identifying phases of matter in future simulations.

Behind certain marginally trapped surfaces one can construct a geometry containing an extremal surface of equal, but not larger area. This construction underlies the Engelhardt-Wall proposal for explaining the Bekenstein-Hawking entropy as a coarse-grained entropy. The construction can be proven to exist classically but fails if the Null Energy Condition is violated. Here we extend the coarse-graining construction to semiclassical gravity. Its validity is conjectural, but we are able to extract an interesting nongravitational limit. Our proposal implies Wall’s ant conjecture on the minimum energy of a completion of a quantum field theory state on a halfspace. It further constrains the properties of the minimum energy state; for example, the minimum completion energy must be localized as a shock at the cut. We verify that the predicted properties hold in a recent explicit construction of Ceyhan and Faulkner, which proves our conjecture in the nongravitational limit.

Machine learning has led to recent advancements in image processing, language translation, finance, robotics, musical and visual arts, and medical diagnosis. In this session, we will explore how machine learning can be applied within fields of physics. We will introduce fundamental concepts in machine learning such a neural networks and supervised vs. unsupervised learning, and then proceed to learn to use tools from Python's TensorFlow library.

Bring your laptop. You can attend remotely via Zoom <https://zoom.us/j/154009181>.

Ghostly neutrino particles continue to bring surprises to fundamental physics, from their existence to the phenomenon of neutrino oscillation which implies that their masses are nonzero. Their exact masses, among the most curious unknowns beyond the Standard Model of particle physics, can soon be probed by the joint analysis of upcoming cosmological surveys including LSST, Euclid, WFIRST, Simons Observatory, and CMB-S4. In this talk, I will first discuss ongoing work studying the effects of massive neutrinos. I will then turn the focus to my major efforts of modeling the challenging nonlinear regime of cosmic structures (<10 Mpc) where neutrino effects are the strongest. Finally, I will draw a roadmap to pin down the neutrino mass over the next decade.

We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. The class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms.
This is joint work with Fernando Brandao (Caltech) and Daniel Stilck Franca (QMATH, Copenhagen).

The asymptotic symmetry charge algebra of certain class of spacetimes could have a nontrivial central extension, which measures the non-equivariance of the charges of the large gauge transformations. The Cardy formula of the dual CFT has been famously used to derive black hole entropy. However, it remains obscure from the point of view of gravity why such a constant on the gravitational phase space could encode the information about the density of black hole micro-states, and what the degrees of freedom accounting for the black hole entropy truly are. I will discuss the ongoing efforts of understanding these questions in the covariant phase space formalism.

There is a close relationship between derived loop spaces, a geometric object, and Hochschild homology, a categorical invariant, made possible by derived algebraic geometry, thus allowing for both intuitive insights and new computational tools.  In the case of a quotient stack, we discuss a "Jordan decomposition" of loops which is made precise by an equivariant localization result.  We also discuss an Atiyah-Segal completion theorem which relates completed periodic cyclic homology to Betti cohomology.

There is a profound lack of diversity in science labs and classrooms, which has a negative impact on productivity. Scientific research demonstrates that diverse groups are more creative and better able to solve problems. Though the perception is that things are improving, NSERC’s recently released report shows that attrition rates in Canadian STEM fields are higher for women than for men at all career stages and that the percentage of women has not changed substantially in the last 15 years. Racialized and Indigenous people are also underrepresented at Canadian universities. This seminar will explore the scientific research surrounding EDI in hiring, writing reference letters, reviewing grants, and managing trainees. Also included are tips and tricks for incorporating EDI into grant applications.

Many free-fermion topological phases can be diagnosed by analyzing a suitable collection of symmetry data. While the Fu-Kane parity criterion for topological insulators is an early example, the systematic generalization to cover all possible crystalline symmetries and their associated topological phases has only recently been achieved. Interestingly, a key step in the generalization is to recognize the importance of understanding the entanglement-free product states: once these trivial phases are completely mapped, the topological ones are naturally exposed as the “remainders.” In this talk, we will first introduce the theory of symmetry indicators for topological (crystalline) insulators and semimetals, and then discuss how it can be generalized to cover superconductors.