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Content archived on 2024-06-18

Isoperimetric and Concentration Inequalities in High-Dimensional Convex Spaces

Objective

"The proposed project lies at the intersection of the local theory of Banach spaces (more precisely ""Asymptotic Geometric Analysis""), Global Riemannian Geometry, and the study of isoperimetric and concentration properties of such spaces. We will study Riemannian manifolds endowed with a probability measure, whose (generalized Ricci) curvature is non-negative (""convex""), or more generally, bounded below (""semi-convex""); an important example is that of the uniform measure on a convex bounded domain in Euclidean space. Despite the immense diversity of these structures, even in the Euclidean case, it is known that they exhibit various unifying geometric and probabilistic properties. In this project, we are interested in various quantitative manifestations of the concentration of measure on these spaces, as their dimension tends to infinity. These include isoperimetric inequalities, providing lower bounds on the boundary measure of sets; Sobolev-type inequalities, such as the classical Poincar\'e (or Spectral-Gap) and logarithmic-Sobolev inequalities; and concentration of measure of various Lipschitz functionals, such as the distance functional. All present conjectures suggest that despite the great diversity, convexity and high-dimensionality serve as unifying forces which render all of these spaces not very different from some canonical ones, like the uniform measure on a Euclidean ball or hyper-cube. In recent years there has been much progress in the analysis of these and related questions. The proposed project intends to deepen and extend our qualitative and quantitative understanding of isoperimetric and concentration inequalities on high-dimensional convex and semi-convex manifolds-with-density in general, and on log-concave measures and convex bodies in particular."

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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.

Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

FP7-PEOPLE-2011-CIG
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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.

MC-CIG - Support for training and career development of researcher (CIG)

Coordinator

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
EU contribution
€ 100 000,00
Address
SENATE BUILDING TECHNION CITY
32000 Haifa
Israel

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Activity type
Higher or Secondary Education Establishments
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Total cost

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.

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