Research database

ReCoMa - Real and Complex Manifolds : Geometry and Holomorphic Dynamics

Duration:
24 months (2023 - 2025)
Principal investigator(s):
Project type:
Nationally funded research - PRIN
Funding body:
MINISTERO (Ministero dell'Università e della Ricerca)
Project identification number:
2022AP8HZ9
PoliTo role:
Partner

Abstract

This project 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 and differential geometric aspects. Geometry of manifolds concerns their analytic, algebraic and metric properties and, on the other side, the study of the topological, differential and holomorphic objects - such as maps, fiber bundles and operators - which can be defined on them. New objects appear in a natural way: self-maps, differential operators, divisors, Jacobian varieties, moduli spaces, etc. The dynamical and analytic properties of those objects reflect then on the geometrical properties of the manifolds. Starting from these considerations, the following general themes identify the scope of this project. 1. Structure of manifolds: Riemannian, Kähler, symplectic, Hermitian, CR manifolds, real and complex analytic spaces, quaternionic analogues, geometry of domains in the different settings, special geometries and holonomy, Einstein metrics, geometric quantization. 2. Maps on manifolds: geometric function theory, discrete and continuous holomorphic dynamics of maps and automorphisms, holomorphic evolution equations, boundary regularity of biholomorphic mappings, immersions and submanifolds, pluripotential theory on Hermitian manifolds, Special Riemannian metrics, Lie groups and homogeneous spaces, representation theory.

People involved

Departments

Partners

  • POLITECNICO DI TORINO
  • Università degli Studi dell'Aquila
  • UNIVERSITA' DEGLI STUDI DI FIRENZE
  • UNIVERSITA' DEGLI STUDI DI PARMA
  • UNIVERSITA' DEGLI STUDI DI TORINO
  • UNIVERSITA' DI ROMA - TOR VERGATA - Coordinator

Keywords

ERC sectors

PE1_5 - Geometry
PE1_4 - Algebraic and complex geometry
PE1_7 - Lie groups, Lie algebras
LS1_1 - Molecular interactions
LS1_10 - Structural biology (NMR)

Sustainable Development Goals

Obiettivo 4. Fornire un’educazione di qualità, equa ed inclusiva, e opportunità di apprendimento per tutti

Budget

Total cost: € 301,000.00
Total contribution: € 187,500.00
PoliTo total cost: € 52,500.00
PoliTo contribution: € 23,440.00