The complex behavior of interacting many-body quantum systems continues to challenge contemporary researchers. In particular, inferring edge dynamics from bulk properties, which typically relies on a bulk-boundary correspondence, remains an unsolved problem in many condensed matter systems. Most edge theories are derived by integrating out bulk matter fields, leaving behind a theory that describes only the edge degrees of freedom. Alternatively, when a suitable hydrodynamic theory for the system is developed, the relationship between bulk matter fields and edge dynamics naturally follows from "classical" hydrodynamic boundary conditions, such as no-penetration and no-stress. If a system admits an effective theory in terms of a single complex scalar, such as an order parameter or wavefunction, constructing a hydrodynamic theory becomes straightforward, with boundary conditions arising directly from conservation laws. In this talk I will outline this general process and apply the formalism to three illustrative examples. Fractional Quantum Hall fluids offer insights into hydrodynamic Chern-Simons theories, while polariton fluids motivate the introduction of dissipative effects. Integer quantum Hall states of bosons, representing a type of symmetry-protected topological phase, are effectively described by a two-fluid model which leads to a broader class of boundary conditions and edge modes. Time permitting, I will discuss how this framework may also shed light on turbulence in both quantum and classical systems.

Prof. Kit Windows-Yule has worked with numerous companies, from SME to multinational, spanning 8 industrial sectors, helping to improve both the productivity and sustainability of diverse industrial processes. Through this work, and the interdisciplinary, cross-sectoral learnings facilitated thereby, he has developed transferrable knowledge, tools, and strategies which can be applied to a wide range of scientific and industrial systems. In this talk, he will discuss the most valuable learnings, centering around an experimental-numerical-AI workflow through which systems of interest can be rigorously modelled and optimised according to the needs of, or challenges faced by, a given industrial or academic researcher.

Abstract TBC