### Metric Diophantine approximation: the well approximable theory on manifolds

Velani, S *(University of York)*

Thursday 03 July 2014, 11:30-12:20

Seminar Room 1, Newton Institute

#### Abstract

I will give an overview of recent development regarding the metric theory of well approximable sets restricted to manifold. In particular, I will focus on the strengthening of the fundamental theorems of Khintchine and Gallagher, and demonstrate a basic principle that enables one to establish inhomogeneous extremality from (homogeneous) extermality. The end result of the latter is the inhomogeneous strengthening of the Kleinbock-Margulis theorem that validates the Baker-Sprindzuk Conjecture.

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