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CURVATURE SIGNED

Optimal transport techniques in the geometric analysis of spaces with curvature bounds

Total Cost €

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EC-Contrib. €

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Partnership

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Project "CURVATURE" data sheet

The following table provides information about the project.

Coordinator
THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD 

Organization address
address: WELLINGTON SQUARE UNIVERSITY OFFICES
city: OXFORD
postcode: OX1 2JD
website: www.ox.ac.uk

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Total cost 1˙256˙221 €
 EC max contribution 1˙256˙221 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2018-STG
 Funding Scheme ERC-STG
 Starting year 2019
 Duration (year-month-day) from 2019-02-01   to  2024-01-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD UK (OXFORD) coordinator 1˙178˙128.00
2    THE UNIVERSITY OF WARWICK UK (COVENTRY) participant 78˙092.00

Map

 Project objective

The unifying goal of the CURVATURE project is to develop new strategies and tools in order to attack fundamental questions in the theory of smooth and non-smooth spaces satisfying (mainly Ricci or sectional) curvature restrictions/bounds.

The program involves analysis and geometry, with strong connections to probability and mathematical physics. The problems will be attacked by an innovative merging of geometric analysis and optimal transport techniques that already enabled the PI and collaborators to solve important open questions in the field.

The project is composed of three inter-connected themes:

Theme I investigates the structure of non smooth spaces with Ricci curvature bounded below and their link with Alexandrov geometry. The goal of this theme is two-fold: on the one hand get a refined structural picture of non-smooth spaces with Ricci curvature lower bounds, on the other hand apply the new methods to make progress in some long-standing open problems in Alexandrov geometry.

Theme II aims to achieve a unified treatment of geometric and functional inequalities for both smooth and non-smooth, finite and infinite dimensional spaces satisfying Ricci curvature lower bounds. The approach will be used also to establish new quantitative versions of classical geometric/functional inequalities for smooth Riemannian manifolds and to make progress in long standing open problems for both Riemannian and sub-Riemannian manifolds.

Theme III will investigate optimal transport in a Lorentzian setting, where the Ricci curvature plays a key role in Einstein's equations of general relativity.

The three themes together will yield a unique unifying insight of smooth and non-smooth structures with curvature bounds.

 Publications

year authors and title journal last update
List of publications.
2019 Andrea Mondino, Daniele Semola
Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below
published pages: , ISSN: 0021-7824, DOI: 10.1016/j.matpur.2019.10.005
Journal de Mathématiques Pures et Appliquées 2019-11-22

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