My research interests are in gauge theory and complex geometry, and in particular moduli theory, stability, and mirror symmetry.

I am interested in the general principle in geometry which states that extremal objects in differential geometry correspond to stable objects in algebraic geometry. This principle underlies much of the geometry research of the last 50 years, and there are now many verified instances of it. In particular the Hitchin–Kobayashi correspondence shows that Hermitian Yang–Mills connections (extremal objects) correspond to stable holomorphic vector bundles (stable algebraic objects), and the Chen–Donaldson–Sun theorem asserts that Fano manifolds are Kähler–Einstein (extremal condition) if and only if they are K-stable (stability condition).

I am interested in understanding the generalisations of these two results to new settings, such as investigating different special metrics on vector bundles (such as the deformed Hermitian Yang–Mills equations) or more general special metrics on manifolds (such as constant scalar curvature Kähler (cscK) metrics).