Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory: Exponential Mixing Via Additive Combinatorics
Presenter
March 4, 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
We describe an approach to the problem of exponential mixing of geodesic flows by connecting it to the following general dichotomy: for a given measure on Euclidean space, either its Fourier transform decays polynomially outside a very sparse set of frequencies, or a large subset of the support concentrates near proper subspaces at many scales.