Objective
The project is devoted to innovative directions of research on metric measure spaces (‚mm-spaces’) and synthetic bounds for the Ricci curvature.
It aims to bring together two - currently unrelated - areas of mathematics which both have seen an impressive development in the last decade: i) the study of ,static‘ mm-spaces with synthetic Ricci bounds and ii) the study of Ricci flows for ,smooth‘ Riemannian manifolds. A new ansatz - based on the concept of dynamical convexity - will enable to merge these two cutting-edge developments and will lead to the very first approach to Ricci flows on singular spaces.
The project also aims to break up the limitations for the study of (generalized) Ricci curvature for mm-spaces, until now
being restricted exclusively to spaces with uniform lower bounds for this curvature. For the first time ever, mm-spaces with
(signed) measure-valued lower bounds for the Ricci curvature will be studied - the absolutely continuous, non-constant case being highly innovative as well. Besides Ricci bounds also Ricci tensors will be defined and utilized for novel insights and
sharp estimates.
Furthermore, the project aims to initiate the development of stochastic calculus on mm-spaces and, in particular, to provide pathwise insights into the effect of (singular) Ricci curvature. The focus will be on pathwise optimal coupling, stochastic parallel transport, and derivative formulas. Both the static and the dynamic case are of interest. Methods from optimal transport and from stochastic calculus will be combined to push forward the analysis on path and loop spaces.
Each of these aims is important and worth in its own. Only in combination, however, they produce the dynamics, synergy effects, and cross-fertilization requested for maximum success. The anticipated breakthroughs of the project depend on exceeding classical borders of mathematical disciplines and on merging together topical developments from different fields.
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.
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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.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
ERC-ADG - Advanced Grant
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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) ERC-2015-AdG
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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.
53113 BONN
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.