Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory: Triangle groups: From Hilbert modular varieties to complex dynamics
Presenter
March 7, 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 will discuss the reflection groups associated to hyperbolic triangles from a variety of perspectives: the arithmetic of
their cusps; totally geodesic curves on Hilbert modular surfaces; and Minkowski's question mark function. The latter
arises when triangle groups are mated with polynomials, to produce fractals and dynamical systems on the Riemann sphere.