Objective
"This proposal centers on the special interaction of algebraic and differential geometry which arises from the notion of stability, going back to the celebrated correspondence between polystable vector bundles and Hermite-Einstein connections.
A conjecture of Yau, Tian and Donaldson seeks to extend this correspondence to projective manifolds, formulating an algebro-geometric notion of stability (K-polystability) which should be equivalent to the existence of a (unique) Kaehler metric of constant scalar curvature in the first Chern class of an ample line bundle. The necessity of stability is now settled, thanks to the work of Donaldson, myself (Adv. in Math. 2009) and Mabuchi. The existence implication however seems to be out of reach with current techniques. In this project I will motivate the need to go beyond the notion of K-stability, and select some crucial open problems which arise naturally in this context, especially in connection with Donaldson's program for Fano manifolds and his conjecture that a Fano manifold with a Kaehler-Einstein metric is ``birationally stable"". Another surprising application of algebro-geometric stability to differential geometry has recently emerged in the physical work of Gaiotto, Moore and Neitzke. They showed (conjecturally) how to use the stability and wall-crossing of ``BPS states'' to reconstruct the Hitchin hyperkaehler metric on a class of moduli spaces of Higgs bundles. In this project I propose to study some exciting mathematical questions which arise from this theory.
This project aims at attacking some central problems which stem from the connection between stability and special metrics, and will be carried out by myself as P.I. and Gabor Szekelyhidi as a Team Member, over a period of four years. We will be supported by two Post-Docs (each position lasting two years) and a graduate student (three years)."
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
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.
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.
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.
ERC-2012-StG_20111012
See other projects for this call
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.
Host institution
34136 Trieste
Italy
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.