Hyperplane arrangements and Hodge theory

The Top Heavy Conjecture is an elementary statement about linear algebra that was open for 43 years until its recent proof by Huh and Wang, using fancy algebraic geometry. I will describe this result, along with a related result about certain combinatorially defined polynomials called Kazhdan-Lusztig polynomials of hyperplane arrangements. I will also discuss the generalization of these results to the more abstract setting of matroids.