Geometry, Representation Theory, and the Langlands Program

Schmid and Vilonen have mostly carried out the program of determining the Unitary dual of reductive Lie groups using Hodge theory. Kashiwara and Vilonen solved a long standing conjecture on the microlocal structure of holonomic systems of differential equations, the codimension-three conjecture. Bezrukavnikov has carried out a far reaching generalization of Kazhdan-Lustzig combinatorics to a categorical level. Emerton has made fundamental progress in the p-adic Langlands program by proving a strong local-global compatibility.