Learn Turkish: Kamuoyunun sert tepkisi üzerine bakan istifa etti. - Upon the public's harsh reaction, the minister resigned.

In this context, üzerine acts as a postposition meaning 'upon' or 'as a result of.' It expresses an immediate sequence or a direct response. Grammatically, it requires the noun phrase before it to end with a possessive suffix. Here, that phrase is kamuoyunun sert tepkisi (the public's harsh reaction), which ends with the possessive -si.

Where does the buffer -n- come from in kamuoyunun?

The base word is kamuoyu (public opinion), which is already a compound noun made of kamu (public) and oy (opinion/vote) plus the possessive suffix -u. Because it ends in a possessive vowel, adding the genitive case -un (to mean 'the public's') requires the buffer consonant -n-, making it kamuoyunun.

Since bakan can also mean 'the one who looks', could üzerine bakan mean 'looking upon'?

It is a great thought, as bakan is indeed the present participle of bakmak (to look). However, in this sentence, bakan is simply the noun for 'minister'. The phrase kamuoyunun sert tepkisi üzerine acts as a complete block describing why the action happened, followed by the subject (bakan) and the main verb (istifa etti).

Is üzerine only used for abstract reactions like this?

No, it originally means physically 'onto the top of' something. However, as you reach this level, you will increasingly see it used abstractly to mean 'upon this event happening' or 'in response to this', serving as a handy bridge between a trigger and a reaction.