# Geordie Williamson

**Category: **Research Award Winners

**Affiliation: ** University of Sydney

The 2016 Clay Research Award was made to Geordie Williamson in recognition of his groundbreaking work in representation theory and related fields.

In particular, the award recognises two major breakthroughs. First, his proof, with Ben Elias, of Soergel’s conjecture on bimodules associated to Coxeter groups. This established the combinatorial result that the coefficients of the Kazhdan-Lusztig polynomials are non-negative, as well as yielding a new proof of Kazhdan and Lusztig’s conjectured character formula for representations of complex semi-simple Lie algebras.

The second is the construction (building on earlier work with Ben Elias and Xuhua He) of counterexamples to the expected bounds in Lusztig’s conjectured character formula for rational representations of algebraic groups in positive characteristics that grow exponentially with the rank of the group.