معرفی
Ana Caraiani is a Royal Society University Research Fellow and Professor in the Department of Mathematics at Imperial College London, specializing in Number Theory and Arithmetic Geometry. She is a member of the Number Theory group, focusing on the Langlands program, Shimura varieties, and p-adic Galois representations. Her work bridges arithmetic geometry and representation theory, with contributions to modularity lifting theorems, cohomology of Shimura varieties, and local-global compatibility in the Langlands program.
Education: She earned a Ph.D. in Mathematics from Harvard University in 2012. She held positions as a Veblen Research Instructor (2013–2015) and Veblen Fellow (2015–2016) at the Institute for Advanced Study's School of Mathematics.
Research Interests: Her research emphasizes the classical and p-adic Langlands programs, Shimura varieties, arithmetic geometry, and moduli stacks of Galois representations. Specific topics include vanishing theorems for cohomology, modularity of elliptic curves over CM fields, and applications of perfectoid spaces.
Key Contributions: Caraiani has advanced the proof of modularity of elliptic curves over imaginary quadratic fields, established vanishing theorems for Shimura varieties with torsion coefficients, and contributed to the potential automorphy of Galois representations over CM fields. Her work links geometric approaches to arithmetic conjectures, such as the Sato-Tate and Ramanujan conjectures.
Awards and Recognition: Royal Society University Research Fellowship (202?), Veblen Research Instructor/Fellowships (2013–2016), and contributions to major collaborative projects like the Potential Automorphy over CM Fields paper in the Annals of Mathematics.
