Matthew H. Y. Xie

Kazhdan--Lusztig polynomials for sparse paving matroids are unimodal, with only three exceptions to strict unimodality for rank $\ge 5$.

Speyer’s conjecture on $g$-polynomial coefficient nonnegativity is now proven for all split matroids, cracking a major open problem spanning paving and copaving structures via an unexpected three-term deletion-contraction recurrence.