The project "Geometric Structures on Manifolds and Function Theories" aimed at fostering new interactions among different areas of mathematics, in particular differential geometry and function theory, as well as at strengthening existing collaborations. A complementary objective of the project was to promote the exchange of ideas, techniques and methodologies across different generations of mathematicians, creating a fertile environment for the transmission of knowledge and the development of new research directions. On the geometric side, the project studied manifolds endowed with special structures: symplectic/almost Kähler, (almost) contact (metric), geometric structures inspired by Riemannian holonomy (G2, SU(4), Sp(2), Spin(7)), special metrics on complex manifolds, special curvature conditions on (pseudo-)Riemannian manifolds, twistor techniques in differential geometry, and holomorphic foliations. On the function-theoretical side, the project focused on the theory of complex and hypercomplex analytic functions of one and several variables, with a special attention for their zero sets, their (quasi-)conformal properties, their function spaces, their relation with complex, hypercomplex and quaternionic manifolds.
The principal investigator was Prof. Giovanni Bazzoni (Insubria), who coordinated the work of four units (Insubria, Milano, Ancona and Bari). 6 young researchers were hired full time. The project members and their collaborators produced 53 scientific preprints/publications, which resulted in 64 scientific communications (seminars, workshops and conferences, posters); moreover, 6 conferences and 3 seminar series were organized with the support of the project. The visibility of the project was guaranteed by a kick-off meeting, which took place in Bari 19-20/09/2024 (see https://sites.google.com/view/prin2022/2-days-on-geometric-structures-and-function-theories?authuser=0)
The research unit at Insubria focused on special geometric structures on nilpotent/solvable Lie groups and nilmanifolds/solvmanifolds. The work included the classification of purely coclosed G2 structures on higher-step nilmanifolds, the study of moduli spaces of closed and coclosed G2 structures, the classification of 2-step nilpotent Lie algebras in dimension 8 over algebraically closed fields, and the study of complex solvmanifolds with trivial canonical bundle. The unit also started a project on the construction of nilmanifolds with PSU(3)-structures.
The principal investigator was Prof. Giovanni Bazzoni (Insubria), who coordinated the work of four units (Insubria, Milano, Ancona and Bari). 6 young researchers were hired full time. The project members and their collaborators produced 53 scientific preprints/publications, which resulted in 64 scientific communications (seminars, workshops and conferences, posters); moreover, 6 conferences and 3 seminar series were organized with the support of the project. The visibility of the project was guaranteed by a kick-off meeting, which took place in Bari 19-20/09/2024 (see https://sites.google.com/view/prin2022/2-days-on-geometric-structures-and-function-theories?authuser=0)
The research unit at Insubria focused on special geometric structures on nilpotent/solvable Lie groups and nilmanifolds/solvmanifolds. The work included the classification of purely coclosed G2 structures on higher-step nilmanifolds, the study of moduli spaces of closed and coclosed G2 structures, the classification of 2-step nilpotent Lie algebras in dimension 8 over algebraically closed fields, and the study of complex solvmanifolds with trivial canonical bundle. The unit also started a project on the construction of nilmanifolds with PSU(3)-structures.