  We propose the use of N-jettiness (\tau_N), a global event shape variable, as
a probe of nuclear dynamics in lepton-nucleus collisions. It characterizes the
amount of soft radiation between the jet and nuclear beam directions. We write
down the factorization for the 1-jettiness ($\tau_1$) distribution for the
production of a single hard jet (J) in lepton-nucleus collisions: \ell+A(P) \to
J(P_{J})+X. Each nuclear target gives rise to a unique pattern radiation,
determined by nuclear dynamics, that can be quantified by the
\tau_1-distribution. Up to power corrections, the \tau_1-distribution allows
for a direct measurement of the nuclear PDFs. Additional nuclear-dependent
effects will be dominated through power corrections of size $\sim
Q_s^2(A)/(P_{JT}\tau_1)$ where $Q_s(A)$ is a dynamical scale sensitive to
nuclear medium effects. Such nuclear-dependent effects and the dependence of
Q_s(A) on the nuclear atomic number $A$ can be probed through a dedicated
program of precision measurements of \tau_1-distributions for various nuclei
and kinematics. We give numerical results for the 1-jettiness distribution for
the simplest case of a proton target at next-to-leading-log accuracy.
