Grammatical Question?

kouroshhI wish you the best of luck on your ...

As shown.

CJ

Thank you so much dear Calif. Can we start the sentence with ''Wishing you the best of luck .... or it is grammatically wrong?

kouroshhCan we start the sentence with ''Wishing you the best of luck .... or it is grammatically wrong?

"Wishing you the best of luck on ..." is an abbreviated form of "I am wishing you the best of luck on ...".
As such, it is grammatically wrong, but it has become such a standard practice to omit "I am" in this expression that it is acceptable to

In what context is this being said, and in what sense is "defense" meant? Normally I would wish someone best of luck with something.

I meant PhD defense. Is it correct to use PhD defense at the end of sentence?

I confess I was previously unaware of the term "PhD defense". However, Google results suggest that it is a valid term referring to the examination of a PhD thesis by a committee, and in that case it would would be valid to use in your sentence. I would say "best of luck with your PhD defense", but I am from the UK, and perhaps "on" is more usual in the US.

kouroshhIs it correct to use PhD defense at the end of a sentence?

Yes. ... on your Ph.D. defense.

I wouldn't say it's wrong to use 'with' instead of 'on', but I hear 'on' most of the time.

CJ

Dear CJ, I very much like a way you correct the grammatical errors. For me, personally It is a great way to understand about my mistakes which I do not notice.