Homogenous dynamics, arithmetic and equidistribution

ERC Project HomDyn 833423

General description of our objectives

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 \mathbb {R} / \mathbb{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.

Our team

Name Role
Elon Lindenstrauss PI
Ron Mor PhD student
Omri Solan PhD student
Zvi Shem-Tov Postdoc
Andreas Wieser Postdoc
Taehyeong Kim Postdoc

Former team members

Name Role in project Current position
Weikun He postdoc Assoc. Prof. Chinese Academy of Sciences, Beijing
Or Landesberg PhD student Gibbs Assistant Prof. at Yale
Daren Wei postdoc Assistant Prof. at NUS
Erez Nesharim postdoc Assistant Prof. at Technion
Tsviqa Lakrec PhD student Postdoc at UZH


under constructions

Directions and location