Project description
The interplay between holonomy and geometric flows
Manifolds are topological spaces resembling n-dimensional Euclidean spaces in the vicinity of each point. Lines and curves are 1D manifolds and surfaces are 2D manifolds. Submanifolds generalise the concept of manifold to higher dimensions. Totally geodesic submanifolds and isoparametric hypersurfaces are interesting classes of submanifolds. With the support of the Marie Skłodowska-Curie Actions programme, the HOLYFLOW project aims to investigate the interplay of totally geodesic submanifolds with Riemannian holonomy and isoparametric hypersurfaces with certain geometric flows. The project’s ultimate goal is to obtain results of both intrinsic and extrinsic nature, leveraging both the classical theory of submanifolds in symmetric spaces and expertise in manifolds with special holonomy and geometric flows.
Objective
The geometric objects that can be perceived by our senses are curves and surfaces. Submanifolds provide a natural generalization for higher dimensions of these objects. The focus of this project is on totally geodesic submanifolds and isoparametric hypersurfaces, intriguing classes of submanifolds with connections to various mathematical areas, often studied using differential geometric, algebraic, or topological methods.
The aim of this project is to investigate the interplay of totally geodesic submanifolds with Riemannian holonomy and isoparametric hypersurfaces with certain geometric flows, with the ultimate goal of obtaining results of both intrinsic and extrinsic nature. Specifically, we intend to complete the classifications of totally geodesic submanifolds in symmetric spaces and of homogeneous hypersurfaces in exceptional symmetric spaces. We will also use certain classes of isoparametric hypersurfaces in combination with maximum principles to try to prove an Alexandrov-type theorem in the complex hyperbolic space and long-time existence for the hypersymplectic flow.
To develop this project, the Experienced Researcher will join the Geometric Analysis team at ULB in Brussels, under the supervision of one of its main researchers, Joel Fine. The host group has extensive experience in the study of manifolds with special holonomy and geometric flows, using techniques from PDE theory. The training strategy of this project involves assimilating these techniques. Moreover, the ER has experience in the classical theory of submanifolds in symmetric spaces, as evidenced by his contributions to the field. The combination of both backgrounds is essential for developing this proposal.
Finally, this MSCA fellowship will enhance the convergence of distinct research fields and collaborative networks, generate synergy with the research performed by the Supervisor, diversify the fellow’s mathematical knowledge, and establish him as an independent researcher.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project has not yet been classified with EuroSciVoc.
Be the first one to suggest relevant scientific fields and help us improve our classification service
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2023-PF-01
See all projects funded under this callCoordinator
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
1050 BRUXELLES
Belgium
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.