Objective
The main purpose of this proposal is to explore the canonical models of planar random geometry that have been introduced in the recent years. We call this theory Brownian geometry because one of the central objects, the Brownian map, arises as the universal scaling limit of many discrete models of large random graphs embedded in the plane, in a way very similar to Brownian motion, which is the continuous limit of many different classes of random paths. The preceding scaling limit holds for the Gromov-Hausdorff distance on compact metric spaces. Furthermore, recent developments show that, in addition to its metric structure, the Brownian map can be equipped with a conformal structure.
Our objectives will be to combine the different approaches to develop a systematic study of the Brownian map and its variants called the Brownian disk and the Brownian plane, as well as of the associated discrete models, which are finite graphs embedded in the plane or infinite random lattices such as the uniform infinite planar triangulation. We will also study random phenomena in random geometry, starting with random walks on infinite random lattices, with the ultimate goal of constructing Brownian motion on our continuous models. A question of importance in mathematical physics is to understand the behavior of statistical physics models in random geometry. Another fundamental question is to connect the conformal structure of the Brownian map with the conformal embeddings that are known to exist for discrete planar maps.
The field of random geometry gives rise to exceptionally fruitful interactions between specialists of probability theory, theoretical physicists and mathematicians coming from other areas, in particular from combinatorics. To ensure the best chances of success for the proposed research, we will rely on the expertise of several members of the Laboratoire de Mathématiques d'Orsay, and on the unique environment of Université Paris-Sud and neighboring institutions.
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 applied mathematics mathematical physics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics applied mathematics statistics and probability
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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-2016-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.
91190 GIF-SUR-YVETTE
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.