Objective Asymptotic Geometric Analysis is a relatively new field, the young finite dimensional cousin of Banach Space theory, functional analysis and classical convexity. It concerns the {\em geometric} study of high, but finite, dimensional objects, where the disorder of many parameters and many dimensions is ``regularized'' by convexity assumptions. The proposed research is composed of several connected innovative studies in the frontier of Asymptotic Geometric Analysis, pertaining to the deeper understanding of two fundamental notions: Polarity and Central-Symmetry. While the main drive comes from Asymptotic Convex Geometry, the applications extend throughout many mathematical fields from analysis, probability and symplectic geometry to combinatorics and computer science. The project will concern: The polarity map for functions, functional covering numbers, measures of Symmetry, Godbersen's conjecture, Mahler's conjecture, Minkowski billiard dynamics and caustics. My research objectives are twofold. First, to progress towards a solution of the open research questions described in the proposal, which I consider to be pivotal in the field, including Mahler's conjecture, Viterbo's conjecture and Godberesen's conjecture. Some of these questions have already been studied intensively, and the solution is yet to found; progress toward solving them would be of high significance. Secondly, as the studies in this proposal lie at the meeting point of several mathematical fields, and use Asymptotic Geometric Analysis in order to address major questions in other fields, such as Symplectic Geometry and Optimal transport theory, my second goal is to deepen these connections, creating a powerful framework that will lead to a deeper understanding, and the formulation, and resolution, of interesting questions currently unattainable. Fields of science natural sciencesmathematicspure mathematicstopologysymplectic topologynatural sciencescomputer and information sciencesnatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2017-COG - ERC Consolidator Grant Call for proposal ERC-2017-COG See other projects for this call Funding Scheme ERC-COG - Consolidator Grant Coordinator TEL AVIV UNIVERSITY Net EU contribution € 1 514 125,00 Address Ramat aviv 69978 Tel aviv Israel See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all TEL AVIV UNIVERSITY Israel Net EU contribution € 1 514 125,00 Address Ramat aviv 69978 Tel aviv See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
