15:00 Gunter Stolz (UAB Birmingham): From Anderson localization to entanglement bounds
Anderson introduced his model in 1958 in an attempt to understand transport in disordered quantum systems. He greatly simplified the physics by essentially ignoring interaction terms in many-body systems. Only much more recently have the possible effects of interactions on disordered systems and the related concept of many-body localization received increased attention in condensed matter physics and quantum information theory. Here many questions remain wide open, in particular on the side of rigorous work. We will use the simple model of the XY spin chain in random field to illustrate the differences between one-body and many-body localization and to present a few rigorous results.
16:00 Jerry Buckley (King’s College London) A hole theorem for the zero set of the hyperbolic GAF
The hyperbolic Gaussian analytic function (GAF) is a random holomorphic function on the unit disc. It satisfies the remarkable property that the distribution of its zero set is invariant under automorphisms of the disc, and it is essentially the only GAF with this property. A hole is the event that there are no zeroes in a given hyperbolic disc. I will discuss the asymptotic decay of the probability of this event, under various regimes. Joint work with A. Nishry, R. Peled and M. Sodin.