The Federalist Society has posted a review of the oral argument in Mallory v. Norfolk Southern (here):

Under Pennsylvania law, a foreign corporation “may not do business in this Commonwealth until it registers” with the Department of State of the Commonwealth. State law further establishes that registration constitutes a sufficient basis for Pennsylvania courts to exercise general personal jurisdiction over that foreign corporation. Norfolk Southern Railway objected to the exercise of personal jurisdiction, arguing that the exercise violated the Due Process Clause of the Fourteenth Amendment. The trial court agreed and held Pennsylvania’s statutory scheme unconstitutional. The Pennsylvania Supreme Court affirmed. The Supreme Court is to decide if a state registration statute for out-of-state corporations that purports to confer general personal jurisdiction over the registrant violates the Due Process Clause of the Fourteenth Amendment.