Event Detail

Event Type: 
Number Theory Seminar
Date/Time: 
Tuesday, April 12, 2022 - 10:00 to 10:50
Location: 
Zoom only, contact Clayton Petsche for Zoom information

Speaker Info

Institution: 
Reed College
Abstract: 

To every pair (K,c), where K is a quadratic number field and c in K, we associate a directed graph G(K,c) whose vertices are the elements of K having finite orbit under iteration of the polynomial map x\mapsto x^2+c. In a standard analogy between pre-periodic points of polynomial maps and torsion points on abelian varieties, this family of directed graphs corresponds to the family of torsion subgroups of elliptic curves defined over quadratic number fields. In this talk we discuss recent joint work with John Doyle on a classification theorem analogous to known facts about elliptic curves proved by Kamienny and Kenku--Momose.