Geordie Williamson (born 1981 in Bowral, Australia) is an Australian mathematician at the University of Sydney.

For this purpose, they built on works by Wolfgang Soergel and developed a purely algebraic Hodge theory of Soergel bimodules about polynomial rings, In this context, they also succeeded in proving the long-standing positive presumption of positivity for the coefficients of the Kazhdan–Lusztig polynomials for Coxeter groups.

In 1980, Lusztig suggested a character formula for simple modules of reductive groups over fields of finite characteristic p. The conjecture was proved in 1994-95 by a combination of three papers, one by Henning Haahr Andersen, Jens Carsten Jantzen, and Wolfgang Soergel, one by David Kazhdan and George Lusztig and one by Masaki Kashiwara and Toshiyuki Tanisaki for sufficiently large group-specific characteristics (without explicit bound) and later by Peter Fiebig for a very high explicitly stated bound.

Williamson found several infinite families of counterexamples to the generally suspected validity limits of Lusztig's conjecture.

In 2018, he was plenary speaker at the International Congress of Mathematicians in Rio de Janeiro and was elected a Fellow of the Royal Society (FRS) and the Australian Academy of Science.