Michael H. Harris

With Taylor, Harris proved the local Langlands conjecture (first proposed in the 1960's) establishing a correspondence between irreducible smooth representations of GL(n) over a p-adic field and n-dimensional representations the Galois group of that field. He also initiated, and made key contributions to, the proof of the Sato-Tate conjecture (first proposed around 1960) on the distribution of the number of points on a fixed elliptic curve modulo a variable prime number. He initiated the arithmetic use of the higher cohomology of automorphic vector bundles and proved some of the period relations for automorphic forms conjectured by Shimura.