Objective
This project lies at the crossroads of analysis, geometry and probability theory. DiAnQuGe aims to uncover quantitative properties of geometric objects using techniques from functional analysis, harmonic analysis and probability. Specifically, it is dedicated to the following directions:
How well does a given metric space embed in a Banach space or a space with curvature bounds?
In Section 1, I propose to investigate the (in)compatibility of the geometries of finite metrics, including expander-like objects and balls of Carnot groups, with Alexandrov spaces of bounded curvature. Based on a well-established analogy with nonlinear Banach space theory, this will require the development of suitable metric invariants, thus forming a link with discrete analysis. On a related direction, I propose a systematic way to develop such invariants for normed spaces, which will serve as a categorical implementation of Bourgain's proposed Ribe program.
How does the spectrum of a voting system correlate with the behavior of individual voters?
Voting systems are mathematically modeled by functions defined on the vertices of a hypercube in Euclidean space. In Section 2, I propose to utilize input from Fourier analysis, approximation theory and stochastic analysis to further understand the interaction of the spectrum and influences of Boolean functions, along with applications in computer science.
How does a high-dimensional convex set look like?
In Section 3, I propose to investigate sharp behaviors of isoperimetric profiles of convex sets using a mixture of geometric and probabilistic techniques, with a novel component from calculus of variations.
Despite the different origins of these questions, all aforementioned objects share the common feature of having a large-yet-finite dimension, in an appropriate sense. This joint characteristic allows for the transfer of intuition and techniques from one field to the other and has been the driving force behind many recent advances.
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.
This project's classification has been human-validated.
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's classification has been human-validated.
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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HORIZON.1.1 - 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.
HORIZON-ERC - HORIZON ERC Grants
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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-2025-STG
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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.
75794 PARIS
France
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.