  Finite matroids are combinatorial structures that express the concept of
linear independence. In 1964, G.-C. Rota conjectured that the coefficients of
the "characteristic polynomial" of a matroid $M$, polynomial whose coefficients
enumerate its subsets of given rank, form a log-concave sequence. K.
Adiprasito, J. Huh et E. Katz have proved this conjecture using methods which,
although entirely combinatorial, are inspired by algebraic geometry. From the
Bergman fan of the matroid $M$, they define a graded "Chow ring" $A(M)$ for
which they prove analogs of the Poincar\'e duality, the Hard Lefschetz theorem,
and the Hodge--Riemann relations. The sought for log-concavity inequalities are
then analogous to the Khovanskii--Teissier inequalities.
