This project will provide training through research involvement for students and postdoctoral associates in the areas of algebra, algebraic geometry, and number theory. These are some of the oldest branches of mathematics. Current research in these areas is a fascinating mixture of the old and the new: the study of longstanding challenging problems using very modern techniques that intertwine viewpoints from all three areas. Geometry flowered in the third and fourth centuries BC with the study of conic sections by the Greeks; more recent approaches related these geometric objects to quadratic equations. Algebraic geometry is the more general study of geometric objects using polynomials. Number theory is also a very old subject with a history that predates even that of geometry; it is now closely related to algebraic geometry via the study of polynomials with integer coefficients. Research in these fields has had a wide range of applications from elementary particle physics to cybersecurity.
This Research Training Group will help to communicate the excitement of these research areas to students and to foster new research among faculty, postdoctoral associates, and students. The focus of this project is to involve undergraduate students, graduate students, and postdoctoral associates in common research. The investigators plan to achieve these goals by running a colloquium series, by offering topics courses to students, by running a yearly workshop and a yearly conference, and by organizing reading courses among students and postdoctoral associates on topics of current interest.
