Question: Jack Twist is a fictional character of the short story "Brokeback Mountain" by Annie Proulx, where he is portrayed by American actor Jake Gyllenhaal, an American actor, and son of which director?

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Jack Twist: Jack Twist is a fictional character of the short story "Brokeback Mountain" by Annie Proulx and the 2005 Academy Award-winning film adaptation of the same name directed by Ang Lee, where he is portrayed by American actor Jake Gyllenhaal.  Jack's story is depicted by the complex, sexual, and romantic relationship he has with Ennis Del Mar in the American West from 1963 to 1983.

Brokeback Mountain: Brokeback Mountain is a 2005 American neo-western romantic drama film directed by Ang Lee and produced by Diana Ossana and James Schamus.  Adapted from the 1997 short story of the same name by Annie Proulx, the screenplay was written by Ossana and Larry McMurtry.  The film stars Heath Ledger, Jake Gyllenhaal, Anne Hathaway, and Michelle Williams, and depicts the complex emotional and homosexual relationship between Ennis Del Mar and Jack Twist in the American West from 1963 to 1983.

List of accolades received by Brokeback Mountain: "Brokeback Mountain" is a 2005 American epic romantic drama film directed by Ang Lee.  Based on the short story of the same name by author Annie Proulx, the story was adapted by Larry McMurtry and Diana Ossana.  The film depicts the complex emotional and sexual relationship between two men, Ennis Del Mar and Jack Twist (played by Heath Ledger and Jake Gyllenhaal, respectively) in the American West between 1963 and 1983.  Michelle Williams, Anne Hathaway, Linda Cardellini, Randy Quaid, Anna Faris, and Kate Mara feature in supporting roles.

Annie Proulx: Edna Ann Proulx ( ; born August 22, 1935) is an American novelist, short story writer, and journalist.  She has written most frequently as Annie Proulx but has also used the names E. Annie Proulx and E.A. Proulx.

Ennis Del Mar: Ennis del Mar (Del Mar in the film) is the fictional main character of the short story "Brokeback Mountain" by Annie Proulx and the 2005 Academy Award-winning film adaptation of the same name directed by Ang Lee.  Ennis's story is depicted by his complex sexual and romantic relationship with Jack Twist in the American West, over two decades from 1963 to 1983.  In the film, he is portrayed by Heath Ledger, who was nominated for the Academy Award for Best Actor for his performance.

Brokeback Mountain (opera): Brokeback Mountain is an opera by American composer Charles Wuorinen, with a libretto in English by Annie Proulx, based on her 1997 short story "Brokeback Mountain".  They began work on it in 2008 under a commission by Gerard Mortier of the New York City Opera.  He took the project with him to the Teatro Real of Madrid, where the opera was premiered on January 28, 2014.

Brokeback Mountain (short story): "Brokeback Mountain" is a short story by American author Annie Proulx.  It was originally published in "The New Yorker" on October 13, 1997.  "The New Yorker" won the National Magazine Award for Fiction for its publication of "Brokeback Mountain" in 1998.  Proulx won an O. Henry Award prize (third place) for her story in 1998.

Diana Ossana: Diana Lynn Ossana is an American writer who has collaborated on writing screenplays, teleplays, and novels with author Larry McMurtry since they first worked together in 1992, on the semi-fictionalized biography "Pretty Boy Floyd".  She won a Best Adapted Screenplay Oscar or Academy Award, a Writers' Guild of America Award, a BAFTA Award and a Golden Globe Award for her screenplay of Ang Lee's "Brokeback Mountain", along with McMurthy and adapted from the short story of the same name by Annie Proulx.  She is a published author in her own right of several short stories and essays.

Jake Gyllenhaal: Jacob Benjamin Gyllenhaal ( ; born December 19, 1980) is an American actor.  A member of the Gyllenhaal family and the son of director Stephen Gyllenhaal and screenwriter Naomi Foner, Gyllenhaal began acting as a child with a screen debut in "City Slickers" (1991), followed by roles in "A Dangerous Woman" (1993) and "Homegrown" (1998).  His breakthrough performance was as Homer Hickam in "October Sky" (1999) and he garnered an Independent Spirit Award nomination for Best Male Lead for playing the title character in the indie cult hit "Donnie Darko" (2001), in which he played a psychologically troubled teenager alongside his older sister, Maggie Gyllenhaal.  He subsequently appeared in another indie film, "The Good Girl" (2002) and the climate fiction-disaster film "The Day After Tomorrow" (2004), portraying a student caught in a cataclysmic climate event.

Maggie Gyllenhaal: Margalit Ruth "Maggie" Gyllenhaal ( ; born November 16, 1977 in New York City) is an American actress.  Part of the Gyllenhaal family, she is the daughter of filmmakers Stephen Gyllenhaal and Naomi Achs, and the older sister of actor Jake Gyllenhaal.

Supporting paragraphs: Jack Twist Jake Gyllenhaal
Answer: Stephen Gyllenhaal