  The high-energy astrophysical neutrinos recently discovered by IceCube opened
a new way to test Lorentz and CPT violation through the astrophysical neutrino
mixing properties. The flavor ratio of astrophysical neutrinos is a very
powerful tool to investigate tiny effects caused by Lorentz and CPT violation.
There are 3 main findings; (1) current limits on Lorentz and CPT violation in
neutrino sector are not tight and they allow for any flavor ratios, (2)
however, the observable flavor ratio on the Earth is tied with the flavor ratio
at production, this means we can test both the presence of new physics and the
astrophysical neutrino production mechanism simultaneously, and (3) the
astrophysical neutrino flavor ratio is one of the most stringent tests of
Lorentz and CPT violation.
