We have convexity tag - it has empty tag wiki, but I understand the tag broadly as stuff related to convexity, convex functions, convex sets, etc. (Of course, for some of such questions convex-analysis or convex-geometry are more suitable.)

For some time there was concavity tag, see here. The tag was later deleted by an automated process which removed the tags which removes the tags used on single questions after certain time (unless the tag has a tag-wiki). As a result, the question where the tag was created is currently tagged untagged - since it was the only tag there.

I would suggest creating a synonym concavity $\to$ convexity. (After all, these two topics are very close.)

If somebody is willing to write tag-info for convexity, perhaps concavity could be mentioned there, too. (Since the questions in this tag are a bit diverse and I am not really sure what were the original intentions when the tag was created, I don't think I would be able to create a good tag-wiki with clear explanation when this tag is supposed to be used. So I will leave this to more experienced users.)