The deep connections between gauge theory and calibrated geometry, in particular the study of moduli spaces of higher dimensional gauge theories and generalised Seiberg-Witten monopoles are a central focus of my research. Situated at the intersection of differential geometry, geometric analysis and algebraic geometry, my work aims to exploit these connections and develop new methods to construct special holonomy metrics, study their moduli spaces, especially near their boundaries and construct enumerative invariants. Through this research I hope to contribute to a broader understanding of these intricate and fascinating geometric structures.
Dirac Operators on Orbifold Resolutions: Uniform Elliptic Theory (arXiv:2503.08395)
Spin(7)-Orbifold Resolutions (expected 2025)
Preprints are available on request.