Grants and Contributions:

Back to search

Title:

Spaces with sectional and Ricci curvature bounds

Agreement Number:

RGPIN

Agreement Value:

$120,000.00

Agreement Date:

May 10, 2017 -

Organization:

Natural Sciences and Engineering Research Council of Canada

Location:

Ontario, CA

Reference Number:

GC-2017-Q1-03218

Agreement Type:

Grant

Report Type:

Grants and Contributions

Additional Information:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

Recipient's Legal Name:

Kapovitch, Vitali (University of Toronto)

Program:

Discovery Grants Program - Individual

Program Purpose:

Curvature of a space is its most important local geometric invariant. It describes how a space is shaped or curved locally from the point of view of an observer living inside that space.
This proposal is mostly concerned with spaces with various lower curvature bounds. The notions of spaces with lower sectional and Ricci curvature bounds play an important role in a number of fields in mathematics and physics: general relativity, optimal transport, big data analysis and, of course, Riemannian geometry itself. I plan to study several problems concerning generalized spaces with lower sectional curvature bounds (Alexandrov spaces) and generalized spaces with lower Ricci curvature bounds (Restricted Curvature-Dimension condition). I am particularly interested in the interplay between these two conditions which as yet is not sufficiently understood.