Exclusively Federal Jurisdiction
The main subject matters exclusively within the jurisdiction of the federal courts are: admiralty (and more generally all seizures involving international trade), bankruptcy, review of certain federal agency actions, patent cases, copyright cases, federal trademark cases, certain kinds of securities fraud cases, federal crime prosecutions, and lawsuits involving diplomats or members of their families (and related actions against their insurance companies). Almost all cases in which the United States is a party are also handled in federal court.

Source: http://www.dkosopedia.com/wiki/State_Courts