In supersymmetric theories the charged sleptons of different generations may oscillate amongst themselves while they decay. In the case of three generation oscillations, superpartner production at the LHC and NLC may lead to an observable $CP$-violating signal $N(e^+\mu^-) - N(\mu^+e^-)$. This signal is proportional to a $CP$-violating invariant of the slepton mass matrix, $\widetilde{J}$, which is not constrained by searches for the electric dipole moment of the electron. The sensitivity of the LHC and NLC to this signal is highly dependent on superpartner masses, but $\widetilde{J}$ may be probed to a level of $10^{-3}$. Observation of the $CP$-violating signal would imply a definite structure for the slepton mass matrices and have strong implications for models of flavor and SUSY breaking.

We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized 'winding number'. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of 'sign flips' of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural 'dual' of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data