# Colloquium abstracts

**S.G. Dani**

IIT Bombay

February 6, 2014

**Primitive integral solutions for systems of linear inequalities**: The classical Khintchine-Groshev theorems, and their many successors in the metric theory of Diophantine approximations, deal with existence or nonexistence of infinitely many integral solutions for systems of linear inequalities, in terms of given approximating functions on the size of the expected solution. After a review of the results on the topic we discuss the analogous question of existence/nonexistence of infinitely many primitive integral solutions for the systems, when the system is inhomogeneous.