Geometry, Topology and Dynamics Seminar
Hao Xing
CUNY Graduate Center
Equidistribution of polynomially bounded o-minimal curves in homogeneous spaces
Abstract: In a recent joint work with Michael Bersudsky and Nimish Shah, we study the homogeneous equidistribution phenomenon of polynomially bounded o-minimal curves in homogeneous spaces --- in particular, the limiting distribution of $\{ \phi(t) \mathbb Z^n \}$ in the space of unimodular lattices in $\mathbb R^n$, where $\phi(t)$ is an $n \times n$ matrix curve of determinant 1 whose coordinate functions are definable in a polynomially bounded o-minimal structure (which is a large family of functions that includes rational functions and more), and discuss an important condition for this equidistribution to hold. This extends the earlier work of Shah for polynomial trajectories and the work of Peterzil and Starchenko on trajectories on nilmanifolds that are definable in a polynomially bounded o-minimal structure. The talk will be made accessible to a general audience without a background in model theory or homogeneous dynamics.
Wednesday November 5, 2025 at 3:00 PM in 636 SEO