Abstract: The study of log-concave inequalities for combinatorial objects have seen much progress in recent years. One such progress is the solution to the strongest form of Mason's conjecture (independently by Anari et. al. and Brándën-Huh) that the f-vectors of matroid independence complex is ultra-log-concave. In this talk, we discuss a new proof of this result through linear algebra, and discuss generalizations to greedoids and posets. This is a joint work with Igor Pak. This talk is aimed at a general audience.