Anish Ghosh

RESTRICTED SIMULTANEOUS DIOPHANTINE APPROXIMATION

We study the problem of Diophantine approximation on lines in

Badly approximable vectors, curves and number fields

\mathbb{R}^d

Quantitative Diophantine approximation on affine subspaces

under certain primality restrictions.

Dirichlet's Theorem in Function Fields

We show that points on

Recent Trends in Ergodic Theory and Dynamical Systems

C^{1}

Rigidity of measures invariant under semisimple groups in positive characteristic

curves which are badly approximable by rationals in a number field form a winning set in the sense of W. M. Schmidt. As a consequence, we obtain a number field version of Schmidts conjecture.

Shrinking targets for semisimple groups

Recently, Adiceam et.al. (Adv Math 302:231–279, 2016) proved a quantitative version of the convergence case of the Khintchine–Groshev theorem for nondegenerate manifolds, motivated by applications to interference alignment. In the present paper, we obtain analogues of their results for affine subspaces.

DIOPHANTINE APPROXIMATION ON LINES WITH PRIME CONSTRAINTS

We study metric Diophantine approximation for function fields specifically the problem of improving Dirichlets theorem in Diophantine approximation.

A quantitative Oppenheim theorem for generic ternary quadratic forms

We discuss some of the issues that arise in attempts to classify automorphisms of compact abelian groups from a dynamical point of view. In the particular case of automorphisms of one-dimensional solenoids, a complete description is given and the problem of determining the range of certain invariants of topological conjugacy is discussed. Several new results and old and new open problems are described.