Monomial positivity conjecture for Morin singularities

Prove that, for all k and all ℓ ≥ 0, the Thom polynomials Tp(A_k,ℓ) of Morin singularities A_k = C[x]/(x^{k+1}) have nonnegative coefficients in the Chern monomial basis (i.e., exhibit monomial positivity).

Background

Schur positivity is established for many Thom series, but stronger monomial positivity fails for non-Morin types.

The author highlights a longstanding conjecture asserting monomial positivity for the Morin family; despite extensive evidence, this remains unresolved and connects to deep problems such as the Green–Griffiths–Lang conjecture and hyperbolicity.