What are two situations where the us supreme court has original jurisdiction?

In the Judiciary Act of 1789, Congress made the Supreme Court's original jurisdiction exclusive in suits between two or more states, between a state and a foreign government, and in suits against ambassadors and other public ministers. The Supreme Court's jurisdiction over the remainder of suits to which a state was a party was to be concurrent, presumably with state courts since the statute did not expressly confer these cases upon the inferior federal courts

In the 1793 decision in Chisholm v. Georgia , the Supreme Court sparked controversy when it ruled that Article III permitted an original suit in the Supreme Court against a state by a citizen of another state. Congress and the states reacted quickly to what many saw as a threat to the sovereignty of the states and adopted the Eleventh Amendment to the Constitution, which prohibited such suits in the federal courts.