Canonical metrics in Complex Geometry are a fundamental tool to study complex manifolds. Our Villum funded research activities are based on projects focused on the study of such metrics in the Kähler case (which include the famous Käher-Einstein metrics), as well as in the non-Kähler case, where most of even the basic problems remain quite mysterious. In particular, we combine tools ranging from algebraic geometric to geometric analysis to understand the* formation of singularities, degenerations and collapsing* of such canonical metrics. This is related to the constructions of moduli compactifications for spaces of complex varieties.

Some more collegues at AU working in nearby topics we often talk to: G. Bérczi, Z. Dyrefelt, J. Frahm, A. Otiman, A. Swann.

Welcome to the new members: Yanbo Fang and Giuseppe Barbero (with A. Otiman), as postdocs, and Andrés Gomez Villegas, as a PhD student.

- Villum Young Investigator “Complex shapes” (Nov 1st 2018-23, extended 1/2 year). PI C. Spotti.
- Villum YIP+ "Geometry of Collapse" (2023-26). PI C. Spotti.