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Polarity and Central-Symmetry in Asymptotic Geometric Analysis

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.

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry
  • /social sciences/social and economic geography/transport

Call for proposal

ERC-2017-COG
See other projects for this call

Funding Scheme

ERC-COG - Consolidator Grant

Host institution

TEL AVIV UNIVERSITY
Address
Ramat Aviv
69978 Tel Aviv
Israel
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 514 125

Beneficiaries (1)

TEL AVIV UNIVERSITY
Israel
EU contribution
€ 1 514 125
Address
Ramat Aviv
69978 Tel Aviv
Activity type
Higher or Secondary Education Establishments