Geometry, Topology and Dynamics Seminar
Reynold Fregoli
University of Michigan
Ergodic Theorems for Dilates of Curves and Applications to Diophantine Approximation
Abstract: I will start by discussing joint work with P. Bandi and D. Kleinbock on ergodic theorems for dilates of sub-manifolds in mixing $\mathbb{R}^d$-actions – a generalization of spherical averages in ergodic theory. Such theorems have interesting applications to Diophantine approximation: in particular, based on these results, one can show that almost every vector in $\mathbb{R}^d$ is Dirichlet improvable in the multiplicative sense. In the second part of this talk (and time permitting), I will present a further joint work with Jiajun Cheng and Beinuo Guo on the validity of pointwise ergodic theorems as above in connection to the regularity of the test functions.
Wednesday October 22, 2025 at 3:00 PM in 636 SEO