Speaker: Prasuna Bandi
Affiliation: University of Michigan
Title: Ergodic theorem for submanifold actions of $\mathbb{R}^d$ and application to diophantine approximation
Date and Time: May 6, 2025, 16:00:00 Hours
Venue: AG-77
Abstract: Consider a measure preserving action of $\mathbb{R}^d$ on a probability space $(X, \mu)$. Let $M$ be a compact $k$-dimensional $\mathcal{C}^1$ submanifold of $\mathbb{R}^d$ where $1 \leq k \leq d-1$. Under certain assumptions on the action, we prove an effective pointwise ergodic theorem that holds for smooth functions for the action of $M$ on $(X, \mu)$. We use this result to prove a partial analogue of Khintchine’s $0$ – $1$ law in uniform multiplicative Diophantine approximation. This is joint work with Reynold Fregoli and Dmitry Kleinbock.
Affiliation: University of Michigan
Title: Ergodic theorem for submanifold actions of $\mathbb{R}^d$ and application to diophantine approximation
Date and Time: May 6, 2025, 16:00:00 Hours
Venue: AG-77
Abstract: Consider a measure preserving action of $\mathbb{R}^d$ on a probability space $(X, \mu)$. Let $M$ be a compact $k$-dimensional $\mathcal{C}^1$ submanifold of $\mathbb{R}^d$ where $1 \leq k \leq d-1$. Under certain assumptions on the action, we prove an effective pointwise ergodic theorem that holds for smooth functions for the action of $M$ on $(X, \mu)$. We use this result to prove a partial analogue of Khintchine’s $0$ – $1$ law in uniform multiplicative Diophantine approximation. This is joint work with Reynold Fregoli and Dmitry Kleinbock.