To my knowledge, there is currently no default way of doing that at this time.
I believe you would need some intrusion software installed on your computer, maybe Symantec Endpoint Protection, or any Intrusion Detection software that would monitor connection of USB devices. You would also have to configure it to log it.
As for seeing what files were copied, that is difficult without another sort of logging program, but I have not investigated far enough to know which ones you can look into to do such a thing at this time.