Mei Yin’s interest in mathematics and science started early. Through her mother, a university librarian, Yin had access to shelf after shelf of books. Two of her favorites growing up were biographies: one of physicist Marie Curie and the other of Niels Henrik Abel, a Norwegian mathematician whose name now adorns the mathematics equivalent of the Nobel Prize.
Those books, and the lives they describe, made quite an impression on Yin. She would grow up to be a mathematician herself, specializing in statistical physics. “Madame Curie and Abel stand out in my mind particularly because of their tenacity, determination and perseverance,” Yin said. “They, and many other scientists, undoubtedly influenced my decision to become a researcher and to use science — mathematics and physics, in my case — to help the world in whatever way possible.”
Yin will join the Brown faculty in the fall as a Tamarkin Assistant Professor of Mathematics.
Of particular interest in Yin’s work are phase transitions, abrupt changes in the state of a system. Examples include the freezing of liquid water or the temperature at which a molten metal becomes magnetic. The math involved in modeling systems like these is dizzyingly difficult, requiring mathematical techniques for dealing with the immense quantities involved.
One of those techniques — and one of Yin’s specialties — is called renormalization. Yin explains the technique in terms of a lattice beam model. Imagine a three-dimensional grid with vertices connected by lines or beams. The model looks a bit like a series of cubes stacked on top of each other. These lattices are used to model the dynamics of gases, ferromagnetism, and the forces inside the nucleus of an atom. “Since there are so many points on the lattice, it’s very hard to do summations,” Yin said. “With renormalization, what you do is you divide the lattice into different blocks. Then you only sum up the sites within that block. After that, you sum up the blocks. It’s a way to deal with singularities that arise when you do infinite summations.”
Work on renormalization made up the bulk of Yin’s Ph.D. work at the University of Arizona. From there, she became a Bing Instructor at the University of Texas–Austin, where she began to take her research in a new direction.
“When I got to UT–Austin I told my mentors and colleagues I wanted to branch out,” she said. “They wanted to branch out too, so we branched out together.” The new branch was the burgeoning science of exponential random graphs.
Random graphs are used to model networks in the real world — social networks, power grids, and the Internet are examples. The models can also be used in statistical physics, which is what initially interested Yin. Like real-world systems they represent, random graph models undergo phase transitions. As Yin explains it, “A small change in some local quantity in the graph leads to some abrupt, large-scale change in a global quantity.”
Imagine a graph model of a power grid. Sprinkle a broken power line here or there on the graph, and at some point large portions of the network go dark. That’s a phase transition, and Yin has received a grant from the National Science Foundation to develop a quantitative theory of those kinds of transitions in exponential random graph models. Such an insight would have broad application, from statistical physics to modeling of disease outbreaks.
Yin says she’s very much looking forward to continuing her work at Brown. “Brown has a super-strong math department,” she said, “and then there is ICERM (Brown’s NSF-funded math institute), where so many experts come to do research.”
The timing of Yin’s arrival is impeccable, considering her research focus. ICERM is holding a major conference in spring 2014 on network-related questions. “I’m really looking forward to all the interactions,” Yin said.
Call it networking in the service of understanding networks.