What aria is being sung in the movie The Last Station?

The aria being sung in The Last Station is "O mio babbino caro" from the opera Gianni Schicchi by Giacomo Puccini. It's sung by the character of Sophia Tolstoy, played by Helen Mirren, while she's playing the piano in the movie.

This aria is a beautiful and expressive piece, and its use in the film is meant to highlight Sophia's love and devotion to her husband, Leo Tolstoy. The aria's lyrics are about a daughter's longing for her father's approval and affection, which in the context of the movie mirrors Sophia's desire for Tolstoy's love and understanding.