Preperiodic portraits of quadratic polynomials over quadratic fields Anshada Pattambi Muhammedali, OSU Host: John Doyle This is a preliminary research presentation. Talk will be in MS 509 and concurrent on Zoom -- contact Paul Fili for the link.
Abstract: The study of preperiodic points of quadratic polynomials over quadratic fields can be done through the theory of dynamical modular curves. These curves are an important tool in classifying possible quadratic preperiodic portraits and investigating which portraits occur infinitely often. We introduce the main techniques and tools used in this approach, with particular emphasis on dynamical modular curves, and provide an overview of the main result concerning the classification and occurrence of quadratic portraits.
Mathematics Seminars and Colloquia