Is a Master's thesis submitted to the University of California Berkeley in the public domain (i.e., can be shared publicly by a person in USA on the internet without asking anybody's permission)?
No. The general policy of the University of California is that students and faculty retain the copyright of scholarly works they create. So the thesis is copyrighted by its author (unless the author has since transferred copyright for some reason).
However, if you contact the author and ask politely, there is a good chance that they will give you permission to share it.