Talks

Topological factorization homology is an invariant of manifolds which enjoys a hybrid of the structures in topological field theory, and in singular homology.  These invariants are especially interesting when we restrict attention to the factorization homology of surfaces, with coefficients in braided tensor categories.  In this talk, I would like to explain a technique, related to Beck monadicity, which allows us to compute these abstractly defined categories, as modules for explicitly computable, and in many cases well-known, algebras.

The algebras produced in this way for the annulus and punctured torus are the so-called ``reflection equation algebra" and "quantum differential equation algebra", respectively.  When we close up punctures, a variation on the our formalism naturally reproduces the framework of quantum Hamiltonian reduction, and leads to simultaneous deformations of categories D(g/G) of character sheaves on g, on the one hand, and categories QC(Ch_G(T^2)), of quasi-coherent sheaves on the character variety of T^2, on the other.  We call these deformations "quantum character varieties", and they form the two-dimensional part of a four dimensional TFT related to Kapustin-Witten's geometric Langlands TFT, or "topologically twisted N=4 SYM".

I will review recent progress on theory of many-body localization, mostly focusing on properties of the many-body localized phase itself.

I will discuss explicit construction of effective Hamiltonians governing the dynamics of conserved quantities.  The analysis reveals several inequivalent length scales in the system, some of which do not appear to diverge on the approach to the thermalized phase.

Experimental protocols to measure these length scales will also be discussed.

Numerical results suggest that the quantum Hall effect at {\nu} = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at {\nu} =

5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.

In this talk I would like to put forward Wasserstein-geometry as a natural language for Quantum hydrodynamics. Wasserstein-geometry is a formal, infinite dimensional, Riemannian manifold structure on the space of probability measures on a given Riemannian manifold. The basic equations of Quantum hydrodynamics on the other hand are given by the Madelung equations. In terms of Wasserstein-geometry, Madelung equations appear in the shape of Newton's second law of motion, in which the geodesics are disturbed by the influence of a quantum potential. This was pointed out in 2008 by Max. K. von Renesse. Finally, based on the notion of Wasserstein-distance, I will will briefly introduce a natural notion of Shape Space and some of its properties.

We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with Forman weighted combinatorial curvatures and simplicial volumes relying on a decomposition of an abstract simplicial complex into realized embeddings of proper skeletons, we demonstrate model phenomenology such as a minimal volume-scale cutoff, a positive-definite cosmological constant as a regulator for non-degenerate geometries, and naturally emergent simplicial structures from Metropolis network evolution simulations with no restrictions on attachment rules or regular building blocks. Properties which echo results from both the spinfoam formalism and causal dynamical triangulations in quantum gravity will also be illustrated. We conclude with prospects for future investigations into the model, discussing ongoing simulations, modifications to the structure of the theory, and broader applications of the framework.

We'll explain the slogan of the title: a cluster variety is a space associated to a quiver, and which is built out of algebraic tori.

They appear in a variety of contexts in geometry, representation theory, and physics. We reinterpret the definition as: from a quiver (and some additional choices) one builds an exact symplectic 4-manifold from which the cluster variety is recovered as a component in its moduli space of Lagrangian branes. In particular, structures from cluster algebra govern the classification of exact Lagrangian surfaces in Weinstein 4-manifolds.

This is joint work with Vivek Shende and David Treumann.

100 years after the existence of gravitational waves was first postulated by Albert Einstein, the LIGO and Virgo Collaborations detected gravitational waves for the first time on September 14, 2015. The gravitational waves originated from a pair of black holes that merged over one billion years ago.  The merger was so powerful that it shook the very fabric of space and sent a ripple across the Universe that we observed here on Earth at present day. Although this event was but a blip in a sea of data taken by various experiments over the last several decades, it represents a paradigm shift in how we study our Universe.

In this colloquium, I will present some of the history of this great discovery and what it means for our future at the dawn of gravitational wave astronomy.

In quantum theory every state can be diagonalised, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This fact is crucial in quantum statistical mechanics, as it provides the foundation for the notions of majorisation and entropy. A natural question then arises: can we give an operational characterisation of them? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalised: Causality, Purity Preservation, Purification, and Pure Sharpness. If we add the Permutability and Strong Symmetry axioms, which are in fact completely equivalent in theories satisfying the other axioms, the diagonalisation result allows us to define a well-behaved majorisation preorder on states. Indeed this majorisation criterion fully captures the convertibility of states in the operational resource theory of purity where random reversible transformations are regarded as free operations. One can also put forward two alternative notions of purity as a resource: one where free operations are unital channels, and another where free operations are generated by reversible interactions with an environment in the invariant state. Under the validity of the above axioms, all these definitions are in fact equivalent, i.e. they all lead to the same preorder on states, which is given by majorisation, in the very same way as in quantum theory.

Dark matter can be a thermal relic exponentially lighter than
the weak scale without being exponentially weakly coupled. I will present
three mechanisms to obtain light thermal dark matter with sizable
self-interactions and couplings to the Standard Model.

We are currently in an era of precision cosmology, but is it an era of accurate cosmology? By measuring cosmological parameters with many independent probes we can convince ourselves that our measurements of the parameters are indeed correct. Thanks to recent progress, strong gravitational lensing is now a powerful probe of cosmology. In this talk I'll report on a measurement of H0 at 5% precision using two strongly lensed quasars and a 20% measurement on the equation of state of dark energy using a double source plane lens. I'll also present new results from a z=1 strong lensing cluster where the dark matter profile deviates significantly from the NFW profile that is predicted by cold dark matter simulations, but it is consistent with simulations of self-interacting dark matter. I'll finish by discussing how upcoming wide area surveys can provide hundreds of exotic strong lenses that can be used for precise and accurate cosmology over the next decade.

Recent findings on quantitative growth patterns have revealed striking generalities across the tree of life, and recurring over distinct levels of organization. Growth-mass relationships in 1) individual growth to maturity, 2) population reproduction, 3) insect colony enlargement and 4)  community production across wholeecosystems of very different types, often follow highly robust near ¾ scaling laws. These patterns represent some of the most general relations in biology, but the reasons they are so strangely similar across levels of organization remains a mystery. The dynamics of these distinct levels are connected, yet their scaling can be shown to arise independently, and free of system-specific properties. Numerous experiments in prebiotic chemistry have shown that minimal self-replicating systems that undergo template-directed synthesis, typically show reaction orders (ie. growth-mass exponents) between ½ and 1. I will outline how modifications to these simplified reaction schemes can yield growth-mass exponents near ¾, which may offer insight into dynamical connections across hierarchical systems.