Real-rootedness of Chow-ring Hilbert–Poincaré series for arbitrary matroids

Prove that the Hilbert–Poincaré series of the Chow ring of every matroid is a polynomial with only real zeros.

Background

The paper places its main result in the context of a conjecture by June Huh and Matthew Stevens concerning the Hilbert–Poincaré series of Chow rings of matroids. The paper proves the conjecture for uniform geometric lattices, which correspond to uniform matroids, but does not establish the assertion for arbitrary matroids.

References

For example June Huh and Matthew Stevens conjectured that the Hilbert-Poincaré series of the Chow ring and augmented Chow ring of any matroid is a polynomial with only real zeros Conjecture~4.1.3 and 4.3.3.

— Chow polynomials of uniform matroids are real-rooted  (2501.07364 - Brändén et al., 13 Jan 2025) in Section 1, Introduction