Lost and Delirious

When shy and introspective Mary arrives as a new freshman student at an all-girls boarding school, she shares a dorm room with two seniors, Pauline (nicknamed Paulie) and Victoria (nicknamed Tori). In contrast to the timid Mary, Paulie is full of life. For example, at Mary's very first day at the school during a quiet afternoon party on the campus thrown by the staff as a welcome back gathering, Paulie turns the events into a loud music-blasting dance party and spikes the punch with hard liquor. In an effort to break Mary out of her shell, Paulie and Tori involve her in their activities, such as running in the morning. When Mary's roommates learn that her mother recently died, Paulie nicknames her "Mary Brave".
Mary observes the intimacy between her two roommates. Peering out a window at night, she sees them kissing on a roof. At first, she thinks that they are practicing kissing in order to prepare themselves for kissing men, but she soon realises the nature of their romance. This also manifests itself in Paulie coming to Tori's rescue. For example, Paulie defends Victoria from a frustrated math teacher who unintentionally humiliates her when she does not understand a mathematical equation.
When the three are jogging one day, Paulie comes across a hurt falcon, which she befriends. After reading up on falcons, she trains the animal and becomes obsessed with caring for it as she believes that something untoward has happened to its parents. While Paulie tends to the orphaned falcon, Mary and Tori meet some boys from the nearby boys' school. One of the boys, Jake Hollander (Luke Kirby), flirts with Tori, asking if she will be attending her brother's 18th birthday party and making it clear that he is interested in her. When Mary and Tori are alone, Tori expresses disgust at the boy's interest in her, saying, "He liked my tits." When Mary asks if she'll go to the party, Tori says, "And have all those gross guys groping me? No, thanks. I'd rather stay home and do math."
Over time, Paulie and Tori become more comfortable showing affection in front of Mary. It progresses from a quick kiss on the lips in front of her to the two sharing a bed and having sex while they think Mary is sleeping. At first, Mary is shy about sharing a room with the two lovers and feels like an intruder. After a few days, she finds their kissing and murmuring comforting and familiar.
One morning, Victoria's sister, Allison (Emily VanCamp), and her friends rush into the room to wake up the older girls. Paulie is lying in Tori's bed, both naked. Mary pushes Tori's sister out of the room and closes the door. After the younger girls leave, Tori, her head in her hands, decides at that moment to end whatever intimate relationship she had with Paulie, who claims that she loves her. Tori refuses outright, fearing that Alison will tell their parents. Tori then angrily tells Paulie to get out of her bed. When confronted by Allison, Tori tries to extinguish her sister's suspicions by telling her Paulie has an unrequited crush on her and crawled into her bed. Her sister promises to "fix" the rumors about Tori and not tell their parents anything. As she walks away from this conversation, Victoria collapses into tears.
In the library, Victoria explains to Mary that her family is strongly opposed to homosexuality, and she must stop the relationship to prevent their rejection. She creates an image of heterosexuality to her friends and her sister, and then she begins seeing Jake and avoiding Paulie. Mary sympathizes with both of her friends, as she too feels rejected by her father, who does not bother to show up to a father/daughter dance. In the forest at night, Tori and Jake have sex against a tree. Both Mary and Paulie accidentally witness this scene and run back to their room before Tori returns.
When Tori returns to the room, Paulie asks her where she's been and Tori says she was with a friend. Paulie lashes out at her by telling her that she saw what Tori and Jake were doing in the woods. Tori tells Paulie that the intimacy that they had shared will never happen again but she (Tori) would always love her.
Paulie cannot handle Tori's withdrawal from the relationship. She smashes a mirror and hurls a dish cart to the ground and begins to act out in other ways. A rejection letter from the agency that handled Paulie's adoption, which says that her birth mother denied a request from Paulie to get in touch, further sends her over the edge. Upset, Paulie leaves the building and runs into Mrs. Vaughn, with whom she discusses her love for Tory, and Mrs. Vaughn tells her she understands. Paulie then goes on to say "Without her, I would just die."
At the climax, Paulie declares a duel to the death with Jake with fencing swords. Jake is not taking her seriously until he ends up on the ground, with Paulie brandishing a sword above him. She demands that he give up Tori. When he refuses, she stabs him in the leg. Mary rushes to stop her and Paulie runs off. Mary runs to Victoria's soccer match, where the headmistress, math teacher and fellow students are congregated. Upon reaching the group, Mary sees Paulie, sobbing from the top of a building while holding her falcon. Whispering "I rush into the secret house," a Shakespearean reference to suicide, Paulie jumps to her death and the movie ends with the falcon flying in the background.

Question: Who does Paulie duel with?
Answer: Jake