Megilla 11a says "Three ruled over the world - Achav, Achashverosh and Nebuchadnetzar." It suggests a few other names that weren't on the list and rejects them because they didn't rule over one territory or another.
Now, I think it's reasonable to exclude peoples living in the Americas and Australia from "the world" because, as the Gemara discusses above, "from Hodu until Kush" seems to be considered as the whole world, i.e. the Old World. The question becomes, did Achashverosh indeed rule over the "whole (old) world"?
Or were there any peoples, like maybe the Greeks or the Chinese that escaped his rule? For example, in the Greco-Persian Wars, Persia did invade Greece, although they weren't exactly successful. And in China, the Eastern Zhou Dynasty of the time seemed to be isolated from the Persians. Did he rule over them? Are these locations not what the Gemara is talking about (just like it's not talking about the Americas)??
It may also worth considering that the Gemara describes Achashverosh's reign as starting with 7 provinces, expanding to 20 (perhaps the 20 listed in the map below), and finally to 100 provinces (perhaps much more expanded but very temporarily?). However that theory seems to weaken later when the Gemrara says, "Daryavesh established his reign over 120 provinces" (in that he ruled over 7 less than Achashverosh).
Map of Achaemenid Empire at fullest extent: