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Homogenous dynamics, arithmetic and equidistribution

Project description

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.


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.


Net EU contribution
€ 2 090 625,00
Edmond j safra campus givat ram
91904 Jerusalem

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Activity type
Higher or Secondary Education Establishments
Other funding
€ 0,00

Beneficiaries (1)