Kavanaugh’s first day was uneventful. He asked a few questions in both oral arguments. Nothing major.
The removal of the 5 minute Supreme Court line likely ensured the day stayed uneventful. 
Normally, there is a line for people who just want to stand in the back of the chamber and watch the proceedings for 5 minutes or less, with another line for full oral arguments. The 5 minute line was gone today and likely tomorrow, but will likely be back for the November sitting when attention will have shifted to the imminent election.
An order listed was released today:
Mostly denials, but did have an interesting statement from Justice Sotomayor respecting the denial of certiorari in two Eighth Amendment cases regarding solitary confinement. While Sotomayor agreed with the denials on procedural grounds, she iterated that the Supreme Court needs to address the issue of solitary confinement in context of the Eighth Amendment.
The December Calendar was released today:
https://www.supremecourt.gov/oral_arguments/calendars/MonthlyArgumentCalDecember2018.html
Royal v Murphy (Now Carpenter v Murphy) is the most high profile case for December. It regards whether Congress formally disestablished Indian Reservations in what is now Oklahoma. Other cases regard whether the excessive fines provision of the Eighth Amendment is incorporated against the States and whether the court should overrule the “double sovereigns” exception to the Double Jeopardy clause.
