Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory: Effective equidistribution in homogeneous spaces and restricted projection theorems
Presenter
March 5, 2025
Keywords:
- Projection theorems
- Unipotent flows
- Effective equidistribution
- Diophantine approximation
- decoupling theory
MSC:
- 11F66 - Langlands $L$L-functions one variable Dirichlet series and functional equations
- 11J83 - Metric theory
- 22E30 - Analysis on real and complex Lie groups [See also 33C80 43-XX]
- 28A80 - Fractals [See also 37Fxx]
- 37A17 - Homogeneous flows [See also 22Fxx]
- 37C85 - Dynamics induced by group actions other than $\mathbb{Z}$\mathbb{Z} and $\mathbb{R}$\mathbb{R} and $\mathbb{C}$\mathbb{C} [See mainly 22Fxx and also 32M25 57R30 57Sxx]
- 42B15 - Multipliers for harmonic analysis in several variables
- 42B20 - Singular and oscillatory integrals (Calderón-Zygmund
- etc.)
Abstract
I will talk about recent developments on establishing effective versions of Ratner’s equidistribution theorem. I will explain the connection between quantitative behavior of unipotent orbits and problems from harmonic analysis on restricted projections. Then I will explain proofs for some important cases relying on arguments from incidence geometry. Based on joint work with Elon Lindenstrauss, Amir Mohammadi, and Zhiren Wang.