  In this paper, we will outline computations of quantum sheaf cohomology for
deformations of tangent bundles of toric varieties, for those deformations
describable as deformations of toric Euler sequences. Quantum sheaf cohomology
is a heterotic analogue of quantum cohomology, a quantum deformation of the
classical product on sheaf cohomology groups, that computes nonperturbative
corrections to analogues of (27*)^3 couplings in heterotic string computations.
Previous computations have relied on either physics-based GLSM techniques or
computation-intensive brute-force Cech cohomology techniques. This paper
describes methods for greatly simplifying mathematical computations, and
derives more general results than previously obtainable with GLSM techniques.
We will outline recent results (rigorous proofs will appear elsewhere).
