Search for CPT and Lorentz Invariance Violation in Muon g-2

Lorentz symmetry and CPT (Charge-Parity-Time) symmetry are absolute bedrock foundational assumptions of both relativity and quantum field theory. The invariance of these symmetries is axiomatic to our entire structure of modern physics. However, these principles may not be as sacrosanct as we tend to treat them in practice. Violations of CPT and/or Lorentz invariance could be the key to the seeming incompatibility of quantum physics and relativity and could also be responsible for phenomena such as the muon g-2 discrepancy and neutrino oscillations. I will present the formalism for including CPT and Lorentz violating interactions in the Standard Model of particle physics and describe the searches for this physics in the first three years of data from the Fermilab Muon g-2 experiment. Time permitting, I will also preview the first ever search for ultralight dark matter using storage ring muon data.