Objective
The project is concerned with the geometric calculus of variations and its applications in a wide range of fields. I start with fundamental examples of variational problems from geometry and physics, the Bernstein problem for minimal submanifolds of Euclidean spaces, non-abelian Hodge theory as a harmonic map approach to representations of Kähler groups, and Dirac harmonic maps as a mathematical version of the nonlinear supersymmetric sigma model of quantum field theory. These examples will motivate a general regularity and rigidity theory in geometric analysis that will be based in a fundamental way on convexity properties. Convexity will then be linked to concepts of non-positive curvature in geometry, and it will lead me to a general theory of duality relations and convexity. That theory will encompass the formal structures of the new calculus of variations and statistical mechanics, information theory and statistics, and mathematical population genetics in biology. Also, the connection with symmetry principles as arising in high energy theoretical physics will be systematically explored. Further applications lie in material sciences, pattern recognition, and bioinformatics.
The project will thus achieve a novel integration of different disciplines from mathematics and the natural sciences.
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 physical sciences quantum physics quantum field theory
- natural sciences physical sciences classical mechanics statistical mechanics
- natural sciences mathematics pure mathematics geometry
- natural sciences computer and information sciences artificial intelligence pattern recognition
- natural sciences physical sciences theoretical physics
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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-2010-AdG_20100224
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
80539 MUNCHEN
Germany
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.