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Stacking two graphene layers twisted by the ‘magic angle’ 1.1º generates flat energy bands, which in turn catalyzes various strongly correlated phenomena depending on filling and sample details. While this system is most famous for the superconducting and insulating states observed at fractional fillings, I argue that charge neutrality presents an interesting interplay of disorder and interactions.

In scanning tunnelling microscopy (STM), the most striking signature of interactions occurs close to charge neutrality, where the splitting between the flat bands increases dramatically. In analogy with quantum Hall ferromagnetism, I show that this effect may be qualitatively understood as the result of an exchange energy gain. A low-energy manifold of gapped, symmetry-breaking states is identified, one of which possesses quantum valley Hall order. Transport measurements yield ostensibly conflicting information at charge neutrality: while some samples reveal semimetallicity (as expected when correlations are weak), yet others exhibit robust insulation. I reconcile these observations and those of STM by arguing that strong interactions supplemented by weak, smooth disorder stabilize a network of locally gapped quantum valley Hall domains with spatially varying Chern numbers determined by the disorder landscape—--even when an entirely different order is favored in the clean limit. I conclude with a discussion of experimental tests of this proposal via local probes and transport.

In this talk, we present a new outlook on canonical quantum gravity and its coupling to matter.

We will show how this fresh perspective combines the critical elements of holography, loop quantum gravity, and relative locality. I will first focus on the consequences of cutting open a portion of space and show that new symmetry charges and new degrees of freedom reveal themselves. 
I will explain the nature of this boundary symmetry algebra in metric gravity and then first-order gravity. We will see that a rich structure appears that explains from the continuum perspective the non-commutativity of geometric flux, the quantization of the area spectra, the nature of the simplicity constraints but also reveals the dual momentum observables and finally allow to reconcile the elements of canonical gravity with Lorentz invariance.
I will discuss the issue of quantization as a challenge of finding a representation of the boundary algebra and will give clues about where we are in this process.

Let G be a complex reductive group, and X be any smooth projective G-variety. In this talk, we will construct an algebra homomorphism from the G-equivariant homology of the affine Grassmannian Gr_G to the G-equivariant quantum cohomology of X. The construction uses shift operators in quantum cohomologies. We will also discuss the possible extension to the loop rotation equivariant setting and the relation with the Peterson isomorphism when X is the flag variety associated with G. This is based on joint work with Alexander Braverman.

There has long been interest in Beilinson-Bernstein localization for the affine Grassmannian (or affine flag variety). First, Kashiwara-Tanisaki treated the so-called negative level case in the 90's. Some ten years later, Frenkel-Gaitsgory (following work of Beilinson-Drinfeld and Feigin-Frenkel) formulated a conjecture at the critical level and made some progress on it. Their conjecture is more subtle than its negative level counterpart, but also more satisfying. We will review the necessary background from representation theory of Kac-Moody algebras at critical level, formulate the Frenkel-Gaitsgory conjecture, and outline a proof for GL_2. Time permitting, we will discuss how our result provides a test of the Frenkel-Gaitsgory proposal for local geometric Langlands.

You’ve likely heard of quantum computing. Maybe you’re even familiar with the basic principles of how this emerging form of technology harnesses counter-intuitive properties of the subatomic realm to perform tasks that would overwhelm even today’s most powerful “classical” computers. But do you know what that will mean for the ways you work, communicate, play, and live?

Does anyone truly know? Well, no, because some very big challenges remain before quantum computers are commonplace. But for expert perspectives on what the future may hold and how to prepare for the quantum future, you’d be hard-pressed to find a better source than Shohini Ghose.

In her March 4 public lecture at Perimeter Institute, Ghose will guide the audience through the latest advances in the quantum world and share her own journey in quantum science. Ghose, a professor of physics and computer science at Wilfrid Laurier University, studies how the laws of quantum physics can be exploited to transform computing and communications, and to achieve feats such as teleportation.

Ghose is a leading expert, and sought-after speaker, in quantum information science, as well as how to make the global science community more vibrant and inclusive. She is the founding director of the Laurier Centre for Women in Science and President of the Canadian Association of Physicists, and she served as Perimeter Institute’s first Diversity, Equity, and Inclusion Specialist.

Among her many honours, Ghose is a TED Senior Fellow and member of the Royal Society of Canada’s College of New Scholars, Artists, and Scientists. In 2019, she was among 25 leading women scientists from around the world featured in a UNESCO exhibit in Paris.