From the Wolf Foundation:
"At the center of Professor Gregory A. Margulis’s work lies his proof of the Selberg-Piatetskii-Shapiro Conjecture, affirming that lattices in higher rank Lie groups are arithmetic, a question whose origins date back to Poincaré. This was achieved by a remarkable tour de force, in which probabilistic ideas revolving around a non-commutative version of the ergodic theorem were combined with p-adic analysis and with algebraic geometric ideas showing that 'rigidity' phenomena, earlier established by Margulis and others, could be formulated in such a way ('super-rigidity') as to imply arithmeticity. This work displays stunning technical virtuosity and originality, with both algebraic and analytic methods. The work has subsequently reshaped the ergodic theory of general group actions on manifolds. In a second tour de force, Margulis solved the 1929 Oppenheim Conjecture, stating that the set of values at integer points of an indefinite irrational non-degenerate quadratic form in ≥ 3 variables is dense in Rn… A third dramatic breakthrough came when Margulis showed that Kazhdan’s 'Property T' (known to hold for rigid lattices) could be used in a single arithmetic lattice construction to solve two apparently unrelated problems.
Fields Medalist, 1978