Objective
One of the landmark achievements of 20th-century mathematics is the Enriques-Kodaira classification of compact complex surfaces. Yet, for odd Betti number, there is a long-standing open conjecture, known as the Global Spherical Shell (GSS) conjecture, which concerns Class VII surfaces. This remains the main open problem in low-dimensional complex geometry, with the latest advances exploiting deep techniques from algebraic geometry.
Inspired by Perelman’s breakthrough use of Ricci flow in 3-manifolds topology, Streets and Tian introduced a parabolic flow of Hermitian metrics – the pluriclosed flow – which provides a promising analytical approach to the GSS conjecture. Despite the remarkable properties of the flow, well-adapted to the geometry and topology of Class VII surfaces, and its interesting relation to theoretical physics, this approach remains largely unexplored due to important technical difficulties. Recent progress, achieved by García-Fernández with Streets and Jordan, shows how combining advanced analytic techniques with Hitchin’s generalized geometry can overcome these barriers, opening a new research frontier.
SURF FLOW aims at pushing well beyond the analytical approach to the GSS conjecture along this new path, eventually giving new insight for a combined effort with algebraic geometry. I will investigate the evolution of the pluriclosed flow up to its maximal existence time and the formation of singular loci by describing it on a significant class of manifolds. This is the first milestone in the Streets-Tian program for the classification of complex surfaces. Complementing this, I willl study the static points of the flow, which have deep implications to conjectural extensions of Calabi's programme on canonical metrics to complex non-Kähler geometry.
The combination of the supervision by Garcia-Fernandez at ICMAT with the secondment visit to Prof. Streets at UC Irvine, is strategic for the goals of the present proposal.
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.
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
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-2025-PF
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.
28006 Madrid
Spain
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.