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HD-App SIGNED

New horizons in homogeneous dynamics and its applications

Total Cost €

EC-Contrib. €

Partnership

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HD-App project word cloud

Explore the words cloud of the HD-App project. It provides you a very rough idea of what is the project "HD-App" about.

finite sections solution limiting questions euclidean regarding notorious emphasis linear space area give closely suggested last subgroups volume rank deep century suggest objects first expansion central leads presented unbounded geometry discrete diagonal pertaining scaling section distributional forms discussed rational discuss dynamics fraction embark lines theory topological periodic encode analogy algebraic diophantine group systematic continued approximation minkowski variety strategy conjecture infinite lattices homogeneous cubic resisting notably attack orbits resolution integral n special

Project "HD-App" data sheet

The following table provides information about the project.

Coordinator	TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY Organization address address: SENATE BUILDING TECHNION CITY city: HAIFA postcode: 32000 website: www.technion.ac.il contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	Israel [IL]
Total cost	1˙432˙730 €
EC max contribution	1˙432˙730 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2017-STG
Funding Scheme	ERC-STG
Starting year	2018
Duration (year-month-day)	from 2018-10-01 to 2023-09-30

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY Organization address address: SENATE BUILDING TECHNION CITY city: HAIFA postcode: 32000 website: www.technion.ac.il contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	IL (HAIFA)	coordinator	1˙432˙730.00

Map

Project objective

We present a large variety of novel lines of research in Homogeneous Dynamics with emphasis on the dynamics of the diagonal group. Both new and classical applications are suggested, most notably to • Number Theory • Geometry of Numbers • Diophantine approximation.

Emphasis is given to applications in

• Diophantine properties of algebraic numbers.

The proposal is built of 4 sections.

(1) In the first section we discuss questions pertaining to topological and distributional aspects of periodic orbits of the diagonal group in the space of lattices in Euclidean space. These objects encode deep information regarding Diophantine properties of algebraic numbers. We demonstrate how these questions are closely related to, and may help solve, some of the central open problems in the geometry of numbers and Diophantine approximation.

(2) In the second section we discuss Minkowski's conjecture regarding integral values of products of linear forms. For over a century this central conjecture is resisting a general solution and a novel and promising strategy for its resolution is presented.

(3) In the third section, a novel conjecture regarding limiting distribution of infinite-volume-orbits is presented, in analogy with existing results regarding finite-volume-orbits. Then, a variety of applications and special cases are discussed, some of which give new results regarding classical concepts such as continued fraction expansion of rational numbers.

(4) In the last section we suggest a novel strategy to attack one of the most notorious open problems in Diophantine approximation, namely: Do cubic numbers have unbounded continued fraction expansion? This novel strategy leads us to embark on a systematic study of an area in homogeneous dynamics which has not been studied yet. Namely, the dynamics in the space of discrete subgroups of rank k in R^n (identified up to scaling).

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The information about "HD-APP" are provided by the European Opendata Portal: CORDIS opendata.