Learn Farsi: استاد در خصوص چکیده‌ی این نظریه‌ی جدید صحبت می‌کند. - The professor speaks regarding the abstract of this new theory.

All three mean "regarding" or "about," but dar khosus-e sounds more formal and academic than the other two. Since this sentence is about a professor discussing a new theory, this formal tone fits perfectly. You could grammatically use dar moured-e or râje' be, but they are slightly more conversational.

Why is there an ezâfe on chakide right before the word in?

The ezâfe connects the noun chakide to the specific thing it belongs to, forming the phrase "the abstract of this new theory." Even though in is a demonstrative pointing to the theory, the ezâfe on chakide is required to link the first noun to the whole following phrase.

Why do chakide and nazariye take a -ye suffix instead of a simple -e for the ezâfe?

Both of these words end in the silent heh letter. When a Farsi word ends in a silent heh, the ezâfe takes the form of a -ye sound to act as a bridge between the vowels. In written Farsi, this is shown by adding the letter ye to the end of the word.

Does the word chakide specifically mean an academic abstract?

Yes, in an academic or formal context, chakide is the standard word for an abstract. It comes from a verb meaning to drip or to be extracted, so its literal sense is the concentrated essence or summary squeezed out of a larger piece of writing.