Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory: Higher rank Furstenberg slicing
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 upper bounds for the dimensions of the affine and smooth slices of Cartesian products of Cantor sets invariant under multiplication by p_i on the circle. These upper bounds generalize the case of linear slices of products of two invariant Cantor sets, which is the original Furstenberg slicing problem. The higher rank version requires several new tools and ideas. Joint work with Emilio Corso.