Degrees and Honours
MMath (Cam), Ph.D. (Imperial College London)
Research Interests
My research centres around several intimately related branches of differential geometry: Calabi-Yau metrics, special Lagrangians, and special holonomy manifolds. A common theme is to study physics-inspired partial differential equations (eg. Einstein equation, minimal surface equation) in a geometric context with a wealth of additional structures (eg. complex structure, symplectic structure). In particular, I am interested in the Strominger-Yau-Zaslow conjecture, and the Thomas-Yau conjecture.
Select Publications
- A new complete Calabi-Yau metric on C 3 , Inventiones mathematicae, July 2019, Volume 217, Issue 1, pp 1-34.
- A gluing construction of collapsing Calabi-Yau metrics on K3 fibred 3-folds, Geometric and Functional Analysis, August 2019, Volume 29, Issue 4, pp 1002-1047.
- SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family, Acta Math. 229 (2022), no. 1, 1–53.
- Metric SYZ conjecture and non-archimedean geometry, Duke Math. J. 172 (2023), no. 17, 3227–3255.
- Uniqueness of some cylindrical tangent cones to special Lagrangians, joint with Tristan Collins, Geom. Funct. Anal. 33 (2023), no. 2, 376–420.