New Implications of Lorentz Violation

In this proceedings, I summarize two recently discovered theoretical implications that Lorentz violation has on physical systems. First, I discuss new models for neutrino oscillations in which relatively simple combinations of Lorentz-violating parameters can mimic the major features of the current neutrino oscillation data. Second, I will present results on Yang-Mills instantons in Lorentz-violating background fields. An explicit solution is presented for unit winding number in SU(2).