Special Topics in Calamity Physics

Who is Blue Van Meer from Special Topics in Calamity Physics and what is their importance?

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Blue Van Meer is the main character, chief protagonist, and narrator of the novel Special Topics in Calamity Physics by Marisha Pessl. A pretty girl of sixteen who is ahead in school because of her profound intelligence, Blue has traveled around the country with her father, Gareth, a visiting professor of political science. Since the death of Natasha, Blue's mother and Gareth's wife, both father and daughter have never stayed in the same place for more than a few months. Her senior year of high school, Blue is happy to learn that she will get to stay in one place for the entire year - Stockton, North Carolina, where she will attend the culturally-refined Saint Gallway School.
There, Blue meets Hannah Schneider, a film teacher, who brings Blue into a small group of elitist friends who are known as the "Bluebloods.". At first they are wary of Blue, but ultimately come to accept her. At school. Blue has something of a slight romance with a boy named Zach Soderberg, whom she puts off as she becomes more and more drawn into the world of Hannah and the Bluebloods. At a masquerade party that Blue and the Bluebloods sneak into, a man named Smoke Harvey is killed. This seems to upset Hannah, about whom very little is known.
During a camping trip to the Great Smoky Mountains organized by Hannah, Blue finds Hannah dead, hanging from a tree. While everyone writes off Hannah's death as the suicide of a crazy person sent over the edge by the death of Smoke Harvey, Blue isn't convinced. She does research into Hannah's life, ultimately contacting Smoke's family. Ada, Smoke's daughter, reveals that Hannah Schneider is not actually Hannah Schneider, but Catherine Baker, a left wing terrorist responsible for murdering a police officer in the 1980s. She is partly responsible for killing a U.S. senator - Smoke Harvey's uncle - and Smoke, an investigative journalist, has been attempting to unravel the mystery and bring the radicals to justice. Knowing that they are on to her, Hannah arranges to have a masquerade party, during which time, Smoke is killed by other radicals. Hannah herself apparently hoped to stage her disappearance, but accidentally kills herself in the process.
Blue reveals all of these findings to her father, who agrees to go to the police with Blue. But in the morning, Gareth - and all of his clothes - are gone. Blue realizes her father is also a member of the same left wing terrorist group. Blue receives investigative materials from Ada, including an FBI wanted poster. Hannah's picture, as well as her accomplice, George Gracey, are shown. Blue realizes that Gracey is actually one of Gareth's friends, living in Paris. She also learns that her father set up a trust fund for her years before, so Blue will be financially secure as she goes to college.