Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories. Few are exact and inviolable. I will present a new set of methods and sufficient conditions for deriving exact, rigorous, and sharp bounds on all coefficients of hydrodynamic dispersion relations, including diffusivity and the speed of sound. These general techniques combine analytic properties of hydrodynamics and the theory of univalent (complex holomorphic and injective) functions. Particular attention will be devoted to bounds relating transport to quantum chaos, which can be established through pole-skipping in theories with holographic duals. I will also discuss potential applications of univalence methods to bounds without relation to chaos, such as for example the conformal bound on the speed of sound.

* Sašo Grozdanov, University of Ljubljana

The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)

https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09