No. The Middle Ages is the time between the fall of the West Roman Empire and the Modern Age. Alexander's Empire was long gone when the Roman Empire was founded.
Italy is the modern country that was the center of the Roman empire.
The modern country of Peru was the center of the Inca empire.
china
they're empire is in modern day turkey
Iran.
Turkey
Egypt, Iran,
No country has ruled the entire world. However, there have been empires that have ruled the 'known' world from their perspective. Perhaps the first great global ruler was Alexander of Macedonia (Alexander the great) Then there was the Roman Empire The Holey Roman Empire and perhaps the largest of all, The British Empire. In modern times counties/empires seem to be fragmenting rather than growing.
Peru
Alexander the great was born in the empire of Macedonia which would make him a number of modern day nationality's he could of been born in country's such as Bulgaria Macedonia Hungary or Albania.
The area of Alexander the Great's empire encompassed parts of several modern countries, including Greece, Turkey, Egypt, Iran, Iraq, Syria, Jordan, and Afghanistan. His conquests extended from the Hellenic world in the west to the Indus Valley in the east. The empire also included regions of modern-day Pakistan and parts of Central Asia. Overall, Alexander's empire was one of the largest in ancient history, influencing many cultures across these regions.