Defining canonical metrics in high-dimension manifolds
Complex differential geometry is a prominent field of mathematics that stands at the intersection of differential and algebraic geometry. The basic objects are manifolds – spaces that locally look like flat space – and vector bundles over them – a collection of vector spaces parametrised by a manifold. The field is largely concerned with defining optimal notions of distance, so-called canonical metrics. A key question is to determine whether or not a given space has a canonical metric. Funded by the Marie Skłodowska-Curie Actions programme, the CanMetCplxGeom project aims to construct canonical metrics for complex manifolds, holomorphic vector bundles and families of such objects.
Fields of science
- natural sciencescomputer and information sciencescomputational science
- natural sciencesmathematicspure mathematicsgeometry
- natural sciencesmathematicsapplied mathematicsstatistics and probability
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
- natural sciencesmathematicspure mathematicsalgebraalgebraic geometry