Talks

We define an action of the k-strand braid group on the set of cluster variables for the Grassmannian Gr(k,n), provided k divides n. The action sends clusters to clusters, preserving the underlying quivers, defining a homomorphism from the braid group to the cluster modular group for Gr(k,n). Our results can be translated to statements about clusters in Fock-Goncharov configuration spaces of affine flags, provided the number of flags is even. Finally, we apply our results to the two "Grassmannians of finite mutation type," proving in these cases versions of conjectures made by Fomin and Pylyavskyy describing cluster variables as SL_k web invariants. 

With two confident binary black hole mergers already detected in their first observing run, the advanced LIGO detectors are expected to detect hundreds more in coming years.  We are poised to learn more about compact binary (e.g., BNS, NSBH, BBH) formation than ever before, but doing so will demand both detailed characterization of individual events, and inference of the properties of the underlying population as a whole.  I will present the methods behind the detection and characterization of LIGO's binary black hole mergers, what they have taught us about compact binaries thus far, and what they will potentially teach us about compact binary formation in the future.

Topological quantum computing requires phases of matter which host fractionalized excitations that are neither bosons nor fermions. I will present a new route toward realizing such fractionalized phases of matter by literally building on existing topological phases. I will first discuss how existing topological phases, when interfaced with other systems, can exhibit a “topological proximity effect” in which nontrivial topology of a different nature is induced in the neighboring system. Then, I will show how this enables a new entanglement based technique (the “topological bootstrap”) for upgrading topological phases from the integer into the fractional quantum Hall variety. Finally, I will highlight the rich phenomenology of systems with interacting Majorana modes. Such systems can exhibit physics ranging from black hole scrambling to supersymmetry and from alternative surface code architectures to topological phases in three dimensions with completely immobile excitations. I will discuss my plans for understanding both general properties and specific models of such fascinating systems.

The characteristics of black holes smaller than the Planck scale are addressed.  These result from a modified metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution has two interesting features: first, it naturally implies the Generalized Uncertainty Principle. Secondly, this metric exhibits an effective dimensional reduction feature, indicating that the gravitational physics of the sub-Planckian regime is effectively (1+1)-D.

Current constraints on spatial curvature demonstrate it to be dynamically negligible at late times. However, neglecting it as a cosmological parameter would be premature, as it offers a valuable test of eternal inflation models and probes novel large-scale structure phenomena. I will discuss a recent project in which a broad and conservative approach was employed to systematically forecast spatial curvature constraints from a suite of upcoming cosmology surveys, while also examining important degeneracies with cosmological parameters and potential sources of systematic error.

As we get closer to build a quantum computer, the main remaining challenge is handling the noise that aflicts quantum systems.

Topological methods, in their various forms, have become the main contestants in the quest for succesfully overcoming noise. A good deal of their strength and versatility is due to their rather unique physical flavour, which keeps giving rise to surprising developments.

I will discuss the main driving forces behind my research on topological quantum error correction, as well as exciting recent directions, including unexpected connections with high energy physics.