We prove that any two critical circle maps with the same irrational rotation number and the same odd criticality are conjugate to each other by a circle diffeomorphism. The conjugacy is for a full Lebesgue measure set of rotation numbers.
"Rigidity of critical circle maps." Duke Math. J. 167 (11) 2125 - 2188, 15 August 2018. https://doi.org/10.1215/00127094-2018-0017