# Homogenous dynamics, arithmetic and equidistribution

## 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.

### Call for proposal

See other projects for this call

### Host institution

THE HEBREW UNIVERSITY OF JERUSALEM
Edmond J Safra Campus Givat Ram
91904 Jerusalem
Israel
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 2 090 625

### Beneficiaries (1)

THE HEBREW UNIVERSITY OF JERUSALEM
Israel
EU contribution
€ 2 090 625