breakthrough came later in 2005 when she appeared in Ang Lee's Brokeback Mountain, about the romance between two men, Ennis and Jack (played by Heath Ledger and Jake Gyllenhaal, respectively). Impressed with her performance in The Station Agent, the casting director Avy Kaufman recommended Williams to Lee. He found a vulnerability in her and cast her as Alma, the wife of Ennis, who discovers her husband's homosexual infidelity. The actor was emotionally affected by the story and, despite her limited screen time, she was drawn to playing a woman constricted by the social mores of the time. Deeming her a standout among the cast, Ed Gonzalez of Slant Magazine praised Williams for "fascinatingly spiking her unspoken resentment for her sham of a marriage with a hint of compassion for Ennis's secret suffering". Brokeback Mountain proved to be her most widely seen film to that point, grossing $178 million against its $14 million budget. It won three Academy Awards and she received a Best Supporting Actress nomination. Williams began dating Ledger while working on the film. The couple cohabited in Boerum Hill, Brooklyn, New York, and in 2005, she gave birth to their daughter Matilda. 2006–2010: Work with auteurs Williams had two film releases in 2006. She first featured opposite Paul Giamatti in the drama The Hawk Is Dying. Five months after giving birth to her daughter, she returned to work on Ethan Hawke's directorial venture The Hottest State, based on his own novel. Leslie Felperin of Variety found her role to be too brief. Following the awards season success of Brokeback Mountain, Williams was unsure of what to do next. After six months of indecision, she agreed to a small part in Todd Haynes's I'm Not There (2007), a musical inspired by the life of Bob Dylan. She was then drawn to the part of an enigmatic seductress named S in the 2008 crime thriller Deception. The film, which co-starred Hugh Jackman and Ewan McGregor, was considered by critics to be middling and predictable. In her next release, Incendiary, based on Chris Cleave's novel of the same name, Williams reteamed with McGregor to play a woman whose family is killed in a terrorist attack. A reviewer for The Independent called the film "sloppy" and added that Williams deserved better. Williams's two other releases of 2008 were better received. The screenwriter Charlie Kaufman was impressed with her comedic timing in Dick