Opendata, web and dolomites

RicciBounds SIGNED

Metric measure spaces and Ricci curvature — analytic, geometric, and probabilistic challenges

Total Cost €

0

EC-Contrib. €

0

Partnership

0

Views

0

Project "RicciBounds" data sheet

The following table provides information about the project.

Coordinator
RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN 

Organization address
address: REGINA PACIS WEG 3
city: BONN
postcode: 53113
website: www.uni-bonn.de

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 Germany [DE]
 Project website https://wt.iam.uni-bonn.de/erc/home/
 Total cost 2˙430˙000 €
 EC max contribution 2˙430˙000 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-AdG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-09-01   to  2021-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN DE (BONN) coordinator 2˙430˙000.00

Map

 Project 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.

 Publications

year authors and title journal last update
List of publications.
2019 Matthias Erbar, Karl-Theodor Sturm
Rigidity of cones with bounded Ricci curvature
published pages: , ISSN: 1435-9855, DOI:
Journal European Mathematical Society 2019-06-13
2017 Karl-Theodor Sturm
Remarks about Synthetic Upper Ricci Bounds for Metric Measure Spaces
published pages: , ISSN: , DOI:
Arxiv Math 2019-06-13
2018 Yohei Sakurai
One dimensional weighted Ricci curvature and displacement convexity of entropies
published pages: , ISSN: , DOI:
2019-06-13
2017 Nicola Gigli, Chiara Rigoni
A note about the strong maximum principle on RCD spaces
published pages: , ISSN: , DOI:
2019-06-13
2018 Yohei Sakurai
Concentration of 1-Lipschitz functions on manifolds with boundary with Dirichlet boundary condition
published pages: , ISSN: , DOI:
2019-06-13
2018 Janna Lierl, Karl-Theodor Sturm
Neumann heat flow and gradient flow for the entropy on non-convex domains
published pages: , ISSN: 0944-2669, DOI: 10.1007/s00526-017-1292-8
Calculus of Variations and Partial Differential Equations 57/1 2019-06-13
2018 Nicola Gigli, Luca Tamanini
Second order differentiation formula on RCD$(K,N)$ spaces
published pages: 377-386, ISSN: 1120-6330, DOI: 10.4171/RLM/811
Rendiconti Lincei - Matematica e Applicazioni 29/2 2019-06-13
2018 Angelo Profeta, Karl-Theodor Sturm
Heat Flow with Dirichlet Boundary Conditions via Optimal Transport and Gluing of Metric Measure Spaces
published pages: , ISSN: , DOI:
Arxiv Math 2019-06-13
2017 Bang-Xian Han
Ricci tensor on smooth metric measure space with boundary
published pages: , ISSN: , DOI:
2019-06-13
2018 Nicola Gigli, Luca Tamanini
Benamou-Brenier and duality formulas for the entropic cost on RCD∗(K,N) spaces
published pages: , ISSN: , DOI:
2019-05-24
2017 Fernando Galaz-García, Martin Kell, Andrea Mondino, Gerardo Sosa
On quotients of spaces with Ricci curvature bounded below
published pages: , ISSN: , DOI:
2019-05-24
2017 Bang-Xian Han
Ricci tensor on smooth metric measure space with boundary
published pages: , ISSN: , DOI:
2019-05-24
2018 Bang-Xian Han
Characterizations of monotonicity of vector fields on metric measure spaces
published pages: , ISSN: 0944-2669, DOI: 10.1007/s00526-018-1388-9
Calculus of Variations and Partial Differential Equations 57/5 2019-05-27
2018 Yohei Sakurai
One dimensional weighted Ricci curvature and displacement convexity of entropies
published pages: , ISSN: , DOI:
2019-05-27
2017 Nicola Gigli, Chiara Rigoni
A note about the strong maximum principle on RCD spaces
published pages: , ISSN: , DOI:
2019-05-24
2017 Yohei Sakurai
Comparison geometry of manifolds with boundary under a lower weighted Ricci curvature bound
published pages: , ISSN: , DOI:
2019-05-24
2017 Nicola Gigli, Chiara Rigoni
Recognizing the flat torus among RCD∗(0,N) spaces via the study of the first cohomology group
published pages: , ISSN: , DOI:
2019-05-27
2017 Gerardo Sosa
The isometry group of an ∗-space is Lie
published pages: , ISSN: , DOI:
2019-05-24
2018 Bang-Xian Han
New characterizations of Ricci curvature on RCD metric measure spaces
published pages: 4915-4927, ISSN: 1553-5231, DOI: 10.3934/dcds.2018214
Discrete & Continuous Dynamical Systems - A 38/10 2019-05-24
2018 Yohei Sakurai
Concentration of 1-Lipschitz functions on manifolds with boundary with Dirichlet boundary condition
published pages: , ISSN: , DOI:
2019-05-24
2019 Kei Funano, Yohei Sakurai
Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
published pages: , ISSN: , DOI:
2019-05-27
2017 Karl-Theodor Sturm
Remarks about Synthetic Upper Ricci Bounds for Metric Measure Spaces
published pages: , ISSN: , DOI:
Arxiv Math 2019-05-27
2019 Matthias Erbar, Karl-Theodor Sturm
Rigidity of cones with bounded Ricci curvature
published pages: , ISSN: 1435-9855, DOI:
Journal European Mathematical Society 2019-05-27
2018 Angelo Profeta, Karl-Theodor Sturm
Heat Flow with Dirichlet Boundary Conditions via Optimal Transport and Gluing of Metric Measure Spaces
published pages: , ISSN: , DOI:
Arxiv Math 2019-05-27

Are you the coordinator (or a participant) of this project? Plaese send me more information about the "RICCIBOUNDS" project.

For instance: the website url (it has not provided by EU-opendata yet), the logo, a more detailed description of the project (in plain text as a rtf file or a word file), some pictures (as picture files, not embedded into any word file), twitter account, linkedin page, etc.

Send me an  email (fabio@fabiodisconzi.com) and I put them in your project's page as son as possible.

Thanks. And then put a link of this page into your project's website.

The information about "RICCIBOUNDS" are provided by the European Opendata Portal: CORDIS opendata.

More projects from the same programme (H2020-EU.1.1.)

iNANOVAC4CANCER (2019)

BIOHYBRID AND BIODEGRADABLE NANOVACCINES FOR CANCER IMMUNOTHERAPY

Read More  

KEYNESGROWTH (2020)

Economic Fluctuations, Productivity Growth and Stabilization Policies: A Keynesian Growth Perspective

Read More  

SuperH (2019)

Discovery and Characterization of Hydrogen-Based High-Temperature Superconductors

Read More