Aspects of hydrodynamic convergence and transport bounds

A closer investigation of the complex analytic structure of correlation functions and dispersion relations has in recent years been able to shed new light on transport and quantum chaos, particularly in holographic theories. In the first part of this talk, I will discuss some new surprising results on the convergence radius of hydrodynamics in holographic theories at finite ’t Hooft coupling. This analysis will proceed, as previously at infinite coupling, via the analysis of complex spectral curves. In the second part of the talk, I will review the construction of the univalence bounds on transport coefficients and outline a set of potentially general observations regarding the univalence properties of diffusion and sound.