## Light leaves and Lusztig’s conjecture

**Advances in Mathematics **(2015) 772-807.
I prove that Lusztig's conjecture reduces to a problem about the light leaves (as defined in my first paper). Using the result in Section 4.3 of this paper (that he discovered independently) Geordie Williamson **disproved Lusztig's conjecture!** The counterexamples grow exponentially in the Coxeter number. Here is Geordie's paper