Project description DEENESFRITPL Building a two-way bridge between the study of dynamical and non-dynamical systems Dynamical systems theory is used to describe the behaviour of complex dynamical systems, studying the nature of the equations of motion of physical systems, such as planetary orbits. But how could non-dynamical systems, for instance arithmetic objects like integer points, be studied using the theory of dynamical systems? The answer is homogeneous dynamics, and the connection goes both ways. The EU-funded HomDyn project was established to extend the tools used in dynamical systems to the study of non-dynamical objects. Researchers will probe the connection between homogeneous dynamics and number theory, arithmetic combinatorics and spectral theory. Show the project objective Hide the project objective Objective We consider the dynamics of actions on homogeneous spaces of algebraic groups,and propose to tackle a wide range of problems in the area, including the central open problems. One main focus in our proposal is the study of the intriguing and somewhat subtle rigidity properties of higher rank diagonal actions. We plan to develop new tools to study invariant measures for such actions, including the zero entropy case, and in particular Furstenberg's Conjecture about $\times 2,\times 3$-invariant measures on $\R / \Z$. A second main focus is on obtaining quantitative and effective equidistribution and density results for unipotent flows, with emphasis on obtaining results with a polynomial error term.One important ingredient in our study of both diagonalizable and unipotent actions is arithmetic combinatorics. Interconnections between these subjects and arithmetic equidistribution properties, Diophantine approximations and automorphic forms will be pursued. Fields of science natural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicsarithmetics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2018-ADG - ERC Advanced Grant Call for proposal ERC-2018-ADG See other projects for this call Funding Scheme ERC-ADG - Advanced Grant Coordinator THE HEBREW UNIVERSITY OF JERUSALEM Net EU contribution € 2 090 625,00 Address Edmond j safra campus givat ram 91904 Jerusalem 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 THE HEBREW UNIVERSITY OF JERUSALEM Israel Net EU contribution € 2 090 625,00 Address Edmond j safra campus givat ram 91904 Jerusalem 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
