A privileged place in the mathematical field of complex differential geometry belongs to Kähler manifolds, which lie at the intersection of complex, symplectic and Riemannian geometry. As a first attempt towards understanding the non-Kähler world, numerous generalizations of Kähler metrics emerged. The project I shall carry out at AIAS for a time frame of three years endeavors to bridge the gap between these geometries by investigating complex non- Kähler manifolds of special type from an analytic and topological point of view.
Specifically, the project comprises a systematic study of explicit examples of manifolds carrying locally conformally Kähler, balanced and pluriclosed metrics and aims at understanding the analytic and cohomological obstructions to the existence of such kind of metrics on generic compact complex manifolds.
My field of study is differential geometry, more precisely, I am interested in complex manifolds carrying special structures. I graduated from University of Bucharest, where I defended my PhD thesis "Conformal Geometry on Hermitian and Symplectic manifolds" in 2017. I held post-doc positions at Max Planck Institut in Bonn, Roma Tre University and University of Florence. I am also a researcher at the Institute of Mathematics of the Romanian Academy.
Project title: Bridging the gap between Kähler and non-Kähler geometry
Area of research: Mathematics
Fellowship period: 1 February 2022 - 31 January 2025