Joint with Leo Patimo. We find a surprisingly beautiful basis of the Hom spaces between indecomposable Soergel bimodules for SL(3) (something that we call "indecomposable light leaves").
Sao Paulo Journal of Mathematical Sciences, 13(2) (2019), 499-538. This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience.
Advances in Mathematics (2015) 772-807. I prove that Lusztig's conjecture reduces to a problem about the light leaves. Using the result in Section 4.3 of this paper Geordie Williamson disproved Lusztig's conjecture! The counterexamples grow exponentially in the Coxeter number. Here is Geordie's paper