Diophantine approximation on the Veronese curve

Abstract: PLEASE NOTE THE UNUSUAL TIME

In the talk we discuss the set $S_n(\lambda)$ of simultaneously $\lambda$-well approximable points in $\mathbb R^n$. That are the points $x$ such that the inequality $|| x - p/q||_\infty < q^{-\lambda - \epsilon}$ has infinitely many solutions in rational points $p/q$. Investigating the intersection of this set with a suitable manifold comprises one of the most challenging problems in Diophantine approximation. It is known that the structure of this set, especially for large $\lambda$, depends on the manifold. For some manifolds it may be empty, while for others it may have relatively large Hausdorff dimension. We will concentrate on the case of the Veronese curve $V_n$. We discuss, what is known about the Hausdorff dimension of the set $S_n(\lambda) \cap V_n$ and will talk about the recent joint results of the speaker and Bugeaud which impose new bounds on that dimension.

number theory

Audience: researchers in the topic

( video )

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Heilbronn number theory seminar

Series comments: This is part of the University of Bristol's Heilbronn number theory seminar. If you wish to attend the talk (and are not a Bristolian), please register using this form or email us at bristolhnts@gmail.com with your name and affiliation (if any).

We will email out the link to all registered participants the day before.

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