Talks

In this talk I will discuss how we might go about about performing a Bell experiment in which humans are used to decide the settings at each end.  The radical possibility we wish to investigate is that, when humans are used to decide the settings (rather than various types of random number generators), we might then expect to see a violation of Quantum Theory in agreement with the relevant Bell inequality.  Such a result, while very unlikely, would be tremendously significant for our understanding of the world (and I will discuss some interpretations).  

Possible radical implications aside, performing an experiment like this would push the development of new technologies.  The biggest problem would be to get sufficiently high rates wherein there has been a human induced switch at each end before a signal as to the new value of the setting could be communicated to the other end and, at the same time, a photon pair is detected.   It looks like an experiment like this, while challenging, is just about feasible with current technologies.  

I will discuss a new class of supersymmetric Wilson loop operators in pure N=2 Yang-Mills-Chern-Simons theory. These Wilson loops preserve one supercharge on-shell and wrap arbitrary Legendrian knots in the standard contact R^3.  I will also explain a relation, motivated by a global picture of contact three-manifolds, between these loop operators and chiral current algebra in two dimensions.  This talk is directly related to, but independent of, my preceding Friday talk in the Mathematical Physics seminar.

A closed quantum system is ergodic and satisfies equilibrium statistical physics when it completely loses local information of its initial condition under time evolution, by 'hiding' the information in non-local properties like entanglement. In the last decade, a flurry of theoretical work has shown that ergodicity can be broken in an isolated, quantum many-body system even at high energies in the presence of disorder, a phenomena known as many-body localization (MBL). In this novel phase of matter, highly excited states of an interacting system can serve as quantum memory and even protect exotic forms of quantum order. Recent claims of experimental observation of MBL in two dimensions using ultra-cold atoms has further raised a plethora of intriguing questions.

In one dimension, the strongly localized regime is described in terms of quasi-local integrals of motion, also known as l-bits. Based on this picture I will describe an efficient tensor network method to efficiently represent the entire spectrum of fully many-body localized systems. This ansatz is also successful at capturing features of the MBL to thermal transition. For higher dimensions, I will develop a refined phenomenology of MBL in terms of l*-bits which are only 'approximately' conserved, based on the stability of the localized phase to perturbations on the boundary. I will conclude with a bird's-eye view of some of the open problems in this rapidly growing field.

The Feynman diagram expansion for a Wilson loop observable in Chern-Simons gauge theory generates an infinite series of topological invariants for framed knots.  In this talk, I will describe a new perturbative formalism which conjecturally generates the same invariants for Legendrian knots in the standard contact R^3.  The formalism includes a `perturbative' localization principle which drastically simplifies the structure of calculations.  As time permits, I will provide some examples and applications.  This talk is based upon joint work with Brendan McLellan and Ruoran Zhang.