Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory: Toral endomorphisms and equidistribution
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 discuss a version of Host's equidistribution theorem on multidimensional tori, giving an essentially optimal result that removed some unnecessary restrictions that appeared in Host's work on the subject. In the commuting case this gives a new proof and an extension of the measure classification theorem of Einsiedler and Lindenstrauss. We also obtain equidistribution results for points drawn from various fractal-type measures on the torus.