Final answer:
The first column should be titled 'Ottoman Empire' and the second column 'Safavid Empire,' representing the Sunni and Shia Muslim empires, respectively, with distinct cultural influences and historical conflicts between them in the 1580s.
Step-by-step explanation:
The appropriate title for the first column of the chart should be "Ottoman Empire." The Ottomans were known for being a Sunni Muslim empire that aimed to expand east and were known for promoting Turkish culture. They did indeed persecute Shia Muslims and lost land to the Safavids in the 1580s.
The appropriate title for the second column should be "Safavid Empire." This empire was known for its efforts to expand west and was comprised of Shia Muslims, promoting Persian culture. The Safavids not only sought to persecute Sunni Muslims but also fought the Ottomans with muskets and cannon in the 1580s, eventually winning these clashes.