You don't have anything in your main. You have to put an infinite loop in there.
Edit:
Also, if you are doing this you then need to invoke the object since the ServerSocket is a part of the class members and not a part of the main. At least I think so, let me double check.
Edit:
Yep, you need to invoke it then. You also need to override the constructor to add a checked exception for the IOException since it won't handle it otherwise.