 Venkatesh has made contributions to a wide variety of areas in mathematics, including number theory, automorphic forms, representation theory, locally symmetric spaces and ergodic theory, by himself, and in collaboration with several mathematicians.Using ergodic methods, Venkatesh, jointly with Jordan Ellenberg, made significant progress on the Hasse principle for integral representations of quadratic forms by quadratic forms.In a series of joint works with Manfred Einsiedler, Elon Lindenstrauss and Philippe Michel, Venkatesh revisited the Linnik ergodic method and solved a longstanding conjecture of Yuri Linnik on the distribution of torus orbits attached to cubic number fields.