The PRIN 2022 project "Real and Complex Manifolds: Geometry and holomorphic dynamics" (code 2022AP8HZ9) aims to combine mathematicians whose research interests are in various aspects of geometry on real and complex manifolds and spaces. We aim to achieve results and give significant contributions in these areas of mathematics, by gathering together expertises from different researchers and promoting the interaction of various methodologies to complement and reinforce each other. The emphasis is on the systematic study of geometric properties of real and complex spaces and functions there defined, with a particular regard to holomorphic dynamics, differential geometric and topological aspects.

The following general themes identify the scope of this project.

• Structure of manifolds: Riemannian, Kahler, symplectic, CR manifolds, real and complex analytic spaces, quaternionic analogues, geometry of domains in the different settings, topology in low dimension, special geometries and holonomy, geometric quantization.

• Maps on manifolds: geometric function theory, discrete and continuous holomorphic dynamics, holomorphic evolution equations, boundary regularity of biholomorphic mappings, immersions and submanifolds, geometric flows, Lie groups and homogeneous spaces, representation theory