Charles Tavis is Avril Incandenza's step brother, Mario Incandenza's father, and James Incandenza's replacement as Headmaster of E.T.A. Tavis suffers from hyper-selfconsciousness, which causes him to be painfully sincere when talking to people. His sincerity is ultimately manipulative and does not allow for genuine connection or empathy with another party. Tavis is a brilliant administrator because he knows that "the key to the successful administration of a top-level junior tennis academy lies in cultivating a kind of reverse-Buddhism, a state of Total Worry" (451).
It is also possible (though unlikely) that the name Charles Tavis is meant to refer to Charles Travis, a philosopher currently on the faculty at Northwestern. Charles Travis has done important work relating to Wittgenstein. References to Wittgenstein and his ideas are all over Wallace's writing, fiction and non-.