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After one lesson, 62-year-old Walter Vale (DeKalb-born Richard Jenkins from “North Country” and “Six Feet Under”) tells his latest piano teacher she need not come back. “If you decide to give up, I’d really like to buy your piano,” she says at the door. She is his fifth teacher. He teaches economics at Connecticut College. His dispassion is pitiable. When a student tries to turn in a paper that’s late due to “personal issues,” Walter says no. With these two spare, sad transactions, writer-director Thomas McCarthy (“The Station Agent”) introduces his main character. Walter will later take on the personal issues of a stranger teaching him how to drum. When Walter goes to a Global Policy and Development conference at NYU to deliver the paper of a colleague who had to cancel, he finds his rarely used apartment occupied by Syrian drummer Tarek (Haaz Sleiman) and Senegalese jeweler Zainab (Danai Gurira). Although they are illegal immigrants, they believed they had rented the place legitimately. It was a con. They apologize to Walter and leave. Later that night he finds the young couple in the street and invites them to stay with him. It’s an apartment he once shared with his late wife, a classical musician. Walter puts off returning to Connecticut so he can drum with Tarek. When Tarek is arrested at a subway turnstile and detained for deportation, Walter takes on his cause. Tarek’s mother Mouna (Hiam Abbass from “Syrian Bride,” “Paradise Now” and “Munich”) arrives from Michigan. She too is welcomed into Walter’s apartment. Opening his door to visitors not welcome in our country opens up Walter’s world. “The Visitor” is a moving study of reciprocal decencies that transcend leases and visas. Yes, a WASP gets rhythm from the Other, but McCarthy makes that exchange amply humane, not trite. With Marian Seldes, Maggie Moore, Michael Cumpsty, Bill McHenry, Richard Kind, Tzahi Moskovitz and Amir Arison. 103m. (Bill Stamets)