My current research is related to complex Kähler geometry. Precisely, I'm interested in the construction and classification of complete Calabi-Yau metrics with nice geometric properties on almost-homogeneous non-compact varieties. The tools involved can range from analysis of complex and real Monge-Ampère equations to algebraic geometry and deformation theory.
Examples of complete Calabi-Yau metrics on affine smoothings of irregular toric Calabi-Yau cones (with Ronan J. Conlon)
K-stable valuations and Calabi-Yau metrics on affine spherical varieties
Journal für die reine und angewandte mathematik (Crelles Journal), 823, 137-171, 2025. [journal version]
accepted by Journal of Differential Geometry.
Journal of Geometric Analysis, 33(7): Paper No. 221, 46 (2023). [journal version]
Annales Polonici Mathematici, 131, 21-56 (2023). [journal version]
Canadian Mathematical Bulletin. vol 64-3, 667 - 677 (2021). [journal version]