Who is Professor Overbrook from Wintergirls and what is their importance?

Professor Overbrook is Lia's father. In her narrative, she sometimes refers to him as "Dad" and sometimes refers to him as "Professor Overbrook." These transitions occur based on the state of their relationship at the time. When he makes an effort to talk to Lia, she refers to him as Dad, but when he is busy with work or arguing with her mother, Lia refers to him as Professor. Although he does his best to deal with his daughter's extreme emotional issues, it is clear that Professor Overbrook is in over his head and in denial about how serious the situation with Lia truly is.