Bergeron–Garsia–Haiman–Tesler nabla positivity conjecture

Let $\lambda$ and $\mu$ be partitions of $n$, let $k\geq 1$, let $\nabla$ be the nabla operator on modified Macdonald polynomials, and let $(\,, \,)$ denote the Hall inner product. Define

$$\iota(\lambda)=\binom{l(\lambda)}{2}-\sum_{\lambda_i<i-1}(i-1-\lambda_i)=\sum_i\min(\lambda_i,i-1),$$

so that $\iota(\lambda)$ is the number of cells of $\lambda$ below the main diagonal. Bergeron–Garsia–Haiman–Tesler's nabla positivity conjecture.

$$(-1)^{\iota(\lambda)}\left(\nabla^k s_{\lambda'},s_\mu\right)\in\mathbb{Z}_{\geq 0}[q,t].$$

This conjecture predicts signed Schur positivity for every power of the nabla operator and motivates the geometric and Tor-theoretic categorifications developed in the paper. The source does not specify whether it has been resolved.