Reference number : GC-2017-Q1-03218, amendment number : , agreement type : G, recipient legal name : Kapovitch, Vitali (University of Toronto), recipient country : CA, recipient province : nan, recipient city : Ontario, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : 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., program purpose french : 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., agreement title english : Spaces with sectional and Ricci curvature bounds, agreement title french : Spaces with sectional and Ricci curvature bounds, agreement number : RGPIN, agreement value : 120000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada