Symmetry as a guide.

Hydrodynamics describes the long-distance evolution of systems with many interacting degrees of freedom. I investigate how anomalies and generalized symmetries constrain fluid dynamics, and how hydrodynamic effective actions emerge from gravity.

Recent work with Mike Blake and Richard Davison connects horizon-preserving diffeomorphisms to symmetries of hydrodynamic actions. My broader work includes chiral magnetohydrodynamics, holographic axial relaxation, real-time lattice simulations and fluctuation effects.

Rational conformal field theories provide exactly tractable models of quantum criticality and connect naturally to topological phases. I study their possible spectra using modular linear differential equations, quasi-characters and coset constructions.

A central aim is to turn modular consistency into practical methods for classifying candidate character vectors and understanding their relation to physical theories. Recent projects explore differential maps across Wronskian sectors and bounds on the signs and growth of quasi-character coefficients.

Symmetry can reveal structure in a quantum state that is invisible to its total entanglement entropy. My work investigates how entanglement decomposes into sectors associated with categorical and non-invertible symmetries.

Using topological defects and boundary states, I study how quantum dimensions and anyonic structure shape sector probabilities and entanglement spectra. Related work explores Verlinde lines, anyon permutations and commutant pairs in conformal field theory.

Background geometry changes the way local observables combine in quantum field theory. I study curved-space operator product expansions and the geometric constraints imposed by conformal symmetry.

With Anatoly Konechny and Naveen B. Umasankar, I use ambient-space methods to distinguish universal curvature effects from theory-dependent CFT data and to understand consistency conditions beyond flat spacetime.