  The $\Delta$-Springer varieties are a generalization of Springer fibers
introduced by Levinson, Woo, and the author that have connections to the Delta
Conjecture from algebraic combinatorics. We prove a positive Hall-Littlewood
expansion formula for the graded Frobenius characteristic of the cohomology
ring of a $\Delta$-Springer variety. We do this by interpreting the Frobenius
characteristic in terms of counting points over a finite field $\mathbb{F}_q$
and partitioning the $\Delta$-Springer variety into copies of Springer fibers
crossed with affine spaces. As a special case, our proof method gives a
geometric meaning to a formula of Haglund, Rhoades, and Shimozono for the
Hall-Littlewood expansion of the symmetric function in the Delta Conjecture at
$t=0$.
