Speaker: Shreyasi Datta
2 December, 2020 14:30 UTC
Abstract: Studying the $p$-adic analogue of Mahler’s conjecture was initiated by Sprind zuk in 1969. Subsequently, there were several partial results culminating in the work of Kleinbock and Tomanov, where the $S$-adic case of the Baker-Sprindzuk conjectures were settled in full generality. We provide a complete $p$-adic analogue of the results of D. Kleinbock on Diophantine exponents of affine subspaces. This answers a conjecture of Kleinbock and Tomanov. Recently, we proved $S$-arithmetic inhomogeneous Khintchine type theorems on analytic nondegenerate manifolds. For $S$ consisting of more than one valuation, the divergence results are new even in the homogeneous setting. This aformentioned result answers questions posed by Badziahin, Beresnevich and Velani and also it generalizes the work of Golsefidy and Mohammadi. In the first half of the talk, I will go over these results and in the seocnd half, I will try to concentrate on some of the technical details of the proofs. The new results presented in this talk are joint work with Anish Ghosh.