Statistical mechanics provides a powerful framework for describing systems composed of many interacting particles.

In regimes where the microscopic details become less relevant, discrete particles can often be replaced by continuous fields, capturing the collective behavior of the system. We explore generalizations of this approach to non-equilibrium systems such as active matter and computational optimization.

A central focus has been, and continues to be, developing and applying boost-agnostic methods - a collection of formalisms where velocity is an observer independent variable - to gain deeper insights into the emergent dynamics of these complex systems.

Hydrodynamics is a particular limit of the collective behavior of systems with large numbers of interacting particles. It applies when short-lived excitations rapidly decay, leaving only slow, long-wavelength perturbations of conserved quantities - such as energy, momentum, and charge - to govern the system’s dynamics. When short lived modes decay quickly the system about a given point can be treated as though it is in thermodynamic equilibrium as defined by the conserved charges - charges then flow between patchs of "local thermodynamic equilibrium".

One of our key research areas is (quasi-)hydrodynamics, an extension of the traditional framework that allows for approximate conservation laws, capturing the dynamics of systems where even conserved currents slowly decay over time. This generalization is essential for understanding a wide range of real-world and theoretical systems beyond the idealized hydrodynamic limit.

Holography - also known as AdS/CFT or gauge/gravity duality - is a correspondence between two very different frameworks rooted in string theory. In particular, holography relates certain observables in strongly coupled quantum field theories to classical perturbations of gravitational theories in one more dimension.

This powerful correspondence allows us to compute observables, such as correlation functions, in strongly coupled theories. This is otherwise difficult to do because of the break-down of perturbation theory. Importantly, such strongly coupled theories rapidly become hydrodynamic in their behaviour.

Our current work focuses on driven steady states within this duality, aiming to understand how non-equilibrium phenomena manifest in both the field theory and its gravitational counterpart.