It's a fine tale, and I thoroughly enjoyed it.
I was hoping to bump its rating up and can not do so! My only options were the following, since it has already reached its maximum "good stuff" ranking of 5: OOC -- inappropriate, given the changes which happened to Harry and Hermione from the time travel ; Illiterate -- nope. It's clearly literate, ; Cliche -- no, it's not a cliche Harry-time-travels story ; Train Wreck, Boring, and Predictable obviously don't apply.
Aha! I have found it:
Oh, this is such a Mary Sue story! "Hermione taught at a Muggle University in Christchurch and became an authority...." : Just what you'd like to be doing, right , Dr. T?
Oops, I think you're already an authority in your field with a Professorship. I don't think "Mary Sue" applies to retroactive wish-fulfillment, when you already got there on your own. :) I suppose I'll also have to avoid applying the "Mary Sue" label to any fourteen-year-old girl who on her own has managed: to become best friends with Harry, Hermione and Ron; to get sorted into Gryffindor; to demonstrate mysterious magical powers; and who at (whatever the age of consent is in her jurisdiction) has already taken the virginity of the Boy Who Lived.
Thanks again for writing.
Trust me, whatever authority I have, it ain't in maths!