Featured papers and preprints

joint with Geordie Williamson, We prove that (sign) parabolic Kazhdan-Lusztig polynomials have non-negative coefficients for ANY Coxeter system and ANY choice of a parabolic subgroup, thus generalizing to the parabolic setting the central result of The Hodge theory of Soergel bimodules by Elias and Williamson.  We also prove a monotonicity conjecture of Brenti. The new techniques were used by Williamson and Lusztig to calculate many new elements of the p-canonical basis and thus make this conjecture.