Skip to main content
Go to the home page of the European Commission (opens in new window)
English English
CORDIS - EU research results
CORDIS

New horizons in homogeneous dynamics and its applications

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).

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.

You need to log in or register to use this function

Keywords

Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)

Programme(s)

Multi-annual funding programmes that define the EU’s priorities for research and innovation.

Topic(s)

Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.

Funding Scheme

Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.

ERC-STG - Starting Grant

See all projects funded under this funding scheme

Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

(opens in new window) ERC-2017-STG

See all projects funded under this call

Host institution

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 1 432 730,00
Address
SENATE BUILDING TECHNION CITY
32000 Haifa
Israel

See on map

Activity type
Higher or Secondary Education Establishments
Links
Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 1 432 730,00

Beneficiaries (1)

My booklet 0 0