Learn Turkish: Otuz yıl sonra, bu okulda eski günleri anıyor olacağız. - Thirty years later, we will be remembering the old days in this school.

It combines the present continuous suffix -ıyor on the main verb anmak (to reminisce) with the future form of the helper verb olmak (to be). Anıyor gives the continuous "remembering" part, and olacağız provides the future "we will be".

I usually use hatırlamak for "to remember". What is the difference with anmak in this sentence?

Hatırlamak is simply the cognitive act of recalling a memory. Anmak, on the other hand, means to commemorate, mention, or actively reminisce about something or someone. In this context, they aren't just recalling the past; they will be actively talking about and celebrating the old days together.

Why does "the old days" take the accusative ending in eski günleri?

Because "the old days" is the specific direct object being reminisced about. You add the accusative suffix -i to günler (days) to show exactly what is receiving the action of the verb anmak.

I see the future suffix -acak in olacağız, but why did the k disappear?

This is consonant mutation. When the first-person plural personal suffix -ız (we) is attached to olacak, the hard k becomes trapped between two vowels and softens into a ğ. So, olacak + -ız becomes olacağız.