The shallow depression between folds on the surface of the brain is called

Correct answer is sulci . 

sulcus is a depression or groove in the cerebral cortex. It surrounds a gyrus (pl. gyri), creating the characteristic folded appearance of the brain in humans and other mammals.

 A sulcus is a shallow groove that surrounds a gyrus, whereas sulci that are larger or deeper are given the term fissures.

The longitudinal fissure is the large furrow which divides the two hemispheres into left and right. A smooth-surfaced cortex would only be able to increase to a certain extent, therefore sulci in the surface area allows for continued growth, overall increasing brain function.

There are two types of sulci which are formed at different times. The primary sulci (e.g. the central sulcus) are formed independently before birth. Secondary sulci, however, are those formed by other factors other than the growth in adjoining areas of the cortex (e.g. the parieto-occipital sulci).

Sulci can also be defined in terms of their depth. A complete sulcus is a sulcus where the groove is very deep (e.g. the collateral sulcus), whereas an incomplete sulcus are not very deep (e.g. the paracentral sulcus).