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.