Daniele Angella

My broad field of research is Complex Geometry. It aims at understanding complex manifolds, namely, certain topological spaces locally modelled on the complex Euclidean space in order to let the notion of holomorphic function be defined. Zero-sets of homogeneous polynomials in the complex projective spaces (which are called projective algebraic manifolds), and their transcendental analogues (the so-called Kähler manifolds) provide special classes of examples and have a very rich theory, where algebra, topology, geometry, and analysis interact towards strong and beautiful properties. On the other side, the broader context of complex (possibly non-Kähler) manifolds yields demanding and interesting mathematical problems, with applications to Theoretical Physics. In the words of de Bartolomeis and Tomassini, “a sort of chemical analysis of symplectic and holomorphic contribution can be successfully performed in order to better understand the role of the different components of the theory” of Kähler Geometry, which “represents a perfect synthesis of the Symplectic and the Holomorphic worlds”. With this in mind, we are ultimately motivated by understanding the structure of complex manifolds towards a sort of classification. In particular, we try to understand cohomological properties or existence of special Hermitian metrics and to find possible obstruction to the topology of complex manifolds. Often, it happens that beautiful constructions and examples shed light on hidden connections between geometry and number theory, topology and analysis!